What is the average rate of change of
g
gg over the interval
−
8
≤
x
≤
−
2
−8≤x≤−2minus, 8, is less than or equal to, x, is less than or equal to, minus, 2?

Answer:

x=2

Step-by-step explanation:

2(4x-1)= -10(x-3)+4

(2×4x)-(1×2 )=(-10×x) -(3×-10) +4

8x -2 = -10x -(-30)+4

8x -2 = -10x +30+4

8x-2= -10x+ 34

8x+10x=34+2

18x=36 we do ÷18

x=2

A 99% confidence interval for an IQ test conducted for a sample of 101 sixth graders, where the sample mean was 104.2, with a standard deviation of 12 is 104.2 ± 3.076.

A 99% confidence interval can be calculated using the formula:

sample mean ± (critical value) x (standard deviation of the mean/ √(sample size))

[tex]sample\ mean\± (critical\ value) ( \frac{standard\ deviation\ of\ the\ mean}{\sqrt{sample\ size} } )[/tex]

To find the critical value, we can use the standard normal distribution table. For a 99% confidence interval, the critical value for a two-tailed test is approximately 2.576.

So, for this problem where sample mean = 104.2 and standard deviation of mean = 12, the 99% confidence interval would be:

104.2 ± 2.576 x (12 / √101)

≈ 104.2 ± 3.076

The standard deviation of the mean is the standard deviation of the sample divided by the square root of the sample size.

This gives us a range of approximately (101.124, 107.276). So we can say that there is a 99% probability that the true population mean IQ score of sixth graders is between 101.122 and 107.276.

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The solution of the partial differential equation 7.7.2 is given by

u(x,t) = t^2 sin(2πx) + c,u(0.3,1.5) = 1.96 + c, where c is an arbitrary constant.

Partial differential equations are mathematical equations used to describe how a function changes as its inputs change. The equation 7.7.2 is a linear second order partial differential equation in two independent variables. It has the form of a generalized wave equation, in which a wave propagates through a medium with varying physical properties.

To calculate partial differential equations u(x,t) for given values of x and t:

Let x = 0.3 and t = 1.5

Substituting these values into the equation, we get:

u(0.3,1.5) = (1.5)^2 sin(2π(0.3)) + c

= 2.25 sin(0.6π) + c

= 2.25(0.87) + c

= 1.96 + c

Therefore, u(0.3,1.5) = 1.96 + c, where c is an arbitrary constant.

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Replace -0.5 with the fraction -1/2 if needed.

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

Explanation:

The legs of any right triangle are always perpendicular. They meet up to form a right angle, aka 90 degree angle.

The line y = 2x+4 goes through (2,8). This can be confirmed with a graph. Or note how plugging x = 2 leads to y = 8.

Therefore, y = 2x+4 forms one of the legs of this triangle.

The slope here is 2 = 2/1; the negative reciprocal is -1/2 = -0.5, which is the slope of the perpendicular line. We want this line to go through (2,8)

So,

y = mx+b

8 = -0.5*2+b

8 = -1+b

8+1 = b

9 = b

b = 9

The equation of the perpendicular line is y = -0.5x+9

Replace -0.5 with the fraction -1/2 if needed.

Check out the graph below.

Dilation is a type of transformation in geometry that changes the size of a shape without changing its orientation. When a shape is dilated by 1 2, it means that the shape is multiplied by a factor of 1 2.

This means that the shape is made half of its original size. The shape will be reduced to one-half of its original area and its perimeter will be halved as well. When a shape is dilated by a factor greater than 1, it will be expanded; when a shape is dilated by a factor less than 1, it will be reduced.

When a shape is dilated by 1 2, the center of dilatation is the same as the original shape's center of dilation. The scale factor of the dilation is 1 2, so the coordinates of the center of dilation will not change.

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The equations can be completed by;

1)  y^8 - 1/y^8

2) 1/y^8 + 1/y^2

We have to know that there are laws that can be used when we are dealing with exponents. Two of the laws that we need to know here are the law of multiplication and the law of division.

Note that;

a^m/a^n = a^m - n (division law)

a^m * a^n = a^ m + n (multiplication law)

Having these laws at the back of our minds;

y^5 y^3 - (y^-2)^4 = y^8 - y^-8

= y^8 - 1/y^8

And;

(y^-2)^4 + y^3/y^5

y^-8 + y^-2

1/y^8 + 1/y^2

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The image of (−8,12) after a dilation is (-2, 3).

A scale factor is a numerical value that can be used to alter the size of any geometric figure or object in relation to its original size. It is used to find the missing length, area, or volume of an enlarged or reduced figure as well as to draw the enlarged or reduced shape of any given figure. It should be remembered that the scale factor only affects how big a figure is, not how it looks.

Given:

Point (-8, 12)

scale factor = 1/4

After applying the scale factor then image

= (-8/4, 12/4)

= (-2, 3)

Hence, the image is (-2, 3).

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While writing the coordinates in the coordinate plane the coordinate that comes first coordinate is represented by x-coordinate.

As given in the question,

In the coordinate plane:

Therefore, the first coordinate in the coordinate plane is represented by x-coordinate.

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A domain is all real numbers if it includes all of the values on the real number line (including negative and positive numbers, fractions, decimals, and irrational numbers).

1. A domain is the set of all possible values of an independent variable that produces a valid solution to a given equation.

2. To determine if a domain includes all real numbers, you must examine the set of values in the domain and see if it includes all the values on the real number line.

3. This includes negative and positive numbers, fractions, decimals, and irrational numbers.

4. If the domain includes all of these, then it is all real numbers.

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Answer:

x=6

Step-by-step explanation:

10x+20=80

10x=60

x=6

Answer:

Slope = 1.25

Y-intercept = -1.5

Step-by-step explanation:

Slope:

[tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}=\frac{11-(-14)}{10-(-10)}=\frac{11+14}{10+10}=\frac{25}{20}=1.25[/tex]

Y-intercept:

[tex]y=mx+b\\\rightarrow y=1.25x+b\\\rightarrow 11=1.25(10)+b\\\rightarrow 11=12.5+b\\\rightarrow -1.5=b[/tex]

Final Equation:

[tex]y=1.25x-1.5[/tex]

Answer:

780.

Step-by-step explanation:

I cant explain Its just the answer.

The answer is 72 boys

The unitary method is a method in which you find the value of a unit and then the value of a required number of units.

Given here: The ratio of boys to girls is 4:3 and total students as 168

thus there are 96 boys and 72 girls and also 3/4 th of the boys study french

which is equivalent to 72 boys

Therefore the number of boys that study spanish is equal to 96-72=24

Hence, 24 boys study spanish.

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[tex]b^2-4ac[/tex] when a is -4. b is -6, and c is 5

Substitute for variables with given values:
[tex]-6^2-4(-4)(5)[/tex]

[tex]=\fbox{116}[/tex]

Answer: 64

Step-by-step explanation:

(47 + 39) - 22

= 86 - 22

= 64

Based on the information provided, the price of each DVD is $11.

To calculate the price of the DVD, two main variables must be considered:

Tax is a compulsory amount that is levied on goods and services by the government. Tax serves as a form of transfer of wealth from the private individuals to the government.

Taxes increase the cost of a good or service.

Now, let's calculate the cost of each DVD:

The price of each DVD = (total cost - tax) / number of DVDs bought

The price of each DVD = (61 - 6) / 5

The price of each DVD = 55 / 5

The price of each DVD = $11

Based on this, the price of each DVD was $11, you can double-check this below
$11 x 5 = $55 (prices for the DVDs) + 6 = $61 (total price)

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To make the given expression x² + 4x + ___ a perfect square ( x + 2)² we must add 4 to the given expression.

As given in the question,

Given expression is equal to :

x² + 4x + ___

Using the formula of perfect square we have :

( a + b )² = a² + 2ab + b²

Here in the given expression x² + 4x + ___

a = x

b = 2

This implies that :

x² + 4x + ___

= x² + 2 ( 2 ) ( x ) + ( 2 )²

= x² + 2 ( 2 ) ( x ) + 4

= ( x + 2 )²

We must add '4' to the given expression.

Therefore, '4' must be added to the given expression x² + 4x + ___ to make it perfect square ( x + 2 )².

The above question is incomplete , the complete question is :

What must be added to the given expression x² + 4x + ___  to make it perfect square ?

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Answer:

114

Explanation:

18.6 rounds up to 19

6.5 rounds down to 6

19 x 6 = 114

Answer:

The answer is (d) y=3x+2

Inserting the given points in the given equation yields the answer. To make the process faster, insert the zero first then you will get y=2. You have to choose whether B and D. Then insert the x values and you will obtain the correct answer which is valid for the given points x and y.

This figure has Line, Point and Rotational Symmetry.

If a figure can be rotated by an angle between 0° and 360° so that the image coincides with the preimage, it has rotational symmetry. The smallest angle for which the figure can be rotated to coincide with itself is the angle of rotational symmetry.

A line of symmetry is a line that divides two equal and symmetrical parts of a shape or object. This line is also known as the axis of symmetry or the mirror line because it divides the figure symmetrically and the divided parts appear to be mirror reflections of each other.

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Answer: If Caleb bought 5/4 of the 12 grams of tea for his mom, we can use the following equation to find out how many grams he got his mom:

5/4 * 12 grams = (5/4) * 12 = 15 grams

So Caleb bought 15 grams of tea for his mom

Step-by-step explanation:

Answer:

I don't know what to say to someone who lost a lot of weight and don't know what to say to someone who lost a lot of weight and don't know what to say to someone who lost a lot of weight and don't know what to say to someone who lost a lot of weight and don't know what to say to someone who lost a lot of weight and don't know what to say to someone who lost a lot of weight and height for all the help and their kids the the other one of it and don't

The Total number of smoothies after calculating are 100 .

What is ratio ?

ratio can be defined as the Given value divided by the total value, is called as ratio.

Given ,

Sally's Smoothies makes two flavors: strawberry and banana. The ratio of strawberry

smoothies to banana smoothies is 3:2.

If Sally makes 60 strawberry smoothies, The number of total smoothies does she make are.

let the banana smoothie be x .

so,

3/2 = 60/x

x = 2* 60 / 3

x = 2*20

x = 40

Total number of smoothies are = 60+40 = 100

Hence , The Total number of smoothies are 100 .

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The constant of proportionality for respective problems is 2/7, 15, 2.75, 13, 4/3.

A) In the first block,

Using points we can find the equation of line ,

Using the formula (y - y₀) = m (x - x₀)

where m is the slope of the equation

The equation of line becomes 2x = 7y

⇒ y = 2/7x

⇒ 2/7 is the constant of proportionality

B) From the graph given,

Again Using the formula (y - y₀) = m (x - x₀)

If we consider two points,

(2,30) and (4,60)

The equation of line becomes

15x = y

Here, the constant of proportionality is 15.

C) It is given the equation is y = 2.75x

The constant of proportionality here is 2.75

D) It is given that,

The price of 5 games is $65.00

The price of 1 game will be 65 / 5

= $13.00

The equation becomes

y = 13x

So, the constant of proportionality becomes 13.

E) Let us consider 2 points (3,12) and (6,24)

The equation of line using the formula (y - y₀) = m (x - x₀) becomes 4x = 3y

⇒ y = 4/3 x

The constant of proportionality becomes 4/3.

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The behavior of the graph relative to the x axis can be described by the equation of the line.

The equation of a line is y = mx + b, where m is the slope and b is the y-intercept. The slope of a line represents the rate of change of the graph with respect to the x axis; a positive slope indicates the graph is increasing, while a negative slope indicates it is decreasing. The y-intercept is the point at which the line crosses the y axis. For example, if the equation of the line is y = 2x + 4, then the slope of the line is 2, meaning the graph increases by 2 units every time the x axis increases by 1 unit, and the y-intercept is 4, meaning the line crosses the y axis at the point (0, 4). By analyzing the equation of the line, you can determine the behavior of the graph relative to the x axis.

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If the model train is 57 cm long, then 266 m is the length of real train.

In the given question, a model train has a scale of 3 cm : 14 m.

If the model train is 57 cm long, then we have to find how long the real train is.

The scale of model train is 3 cm :  14 m.

Now firstly convert m in cm. As we know that 1 m = 100 cm

Now, the scale of model train is 3 cm :  1400 cm.

The length of the model train is 57 cm.

So in the scale of the model train 3 cm = 57 cm

Now the scale of the model train 1 cm = 19 cm

Now find the length of the real train by multiplying the 1400  by 19 because in the scale of 1 cm is equal to the 19 cm.

So, the length of the real train = 1400 × 19

The length of the real train = 26600 cm

The length of the real train = 266 m

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In linear equation , The fifth son is younger than first son will be 31/3. And The age of the fifth son will be 1 and 5/12.

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.  

                                              The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.

In a family, there are five sons. The oldest son is 11 and 3/4 years old, and every next younger brother is younger than the next by 2 and 7/12 years.

Then the fifth son is younger than first son will be

⇒ 4(2 + 7/12)

⇒ 4(31/12)

⇒ (31/3)

The age of the fifth son will be

⇒ (11 + 3/4) – 4(2 + 7/12)

⇒ (47/4) – 4(31/12)

⇒ (47/4) – (31/3)

⇒ 17/12

⇒ 1 + 5/12

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