Look at the table below. Which of the following is the constant rate of change?

Given the question

To resolve this, we can follow the steps below

Step1: Apply the logarithm rule

This will give=>

Since we have been given that

Step2: Substitute the given values into the equation

=>

Answer = 13

Answer:

[tex](f \circ g)(2)=2[/tex]

Step-by-step explanation:

Given functions:

[tex]\begin{cases}f(x)=-2x+8\\g(x)=\sqrt{x+7}\end{cases}[/tex]

The composite function (f o g)(x) means to substitute the function g(x) in place of the x in function f(x).  

Therefore (f o g)(2) means to substitute the result of g(2) in place of the x in the function f(x).

[tex]\begin{aligned}\implies (f \circ g)(2) &=f[g(2)]\\&=f(\sqrt{2+7})\\&=f(\sqrt{9}) \\& = f(3)\\& = -2(3)+8\\&=-6+8\\&=2\end{aligned}[/tex]

The midpoint of (-2, 11) and (18, -1) is:

Point (8,5)

Point D is the centroid of ΔABC, since we know that A.F, BC, and CE are all medians.

A median of a triangle is the line segment that connects the vertex of a triangle to the midpoint of the opposite side. There are usually three medians of a triangle.

The point where the three medians of a triangle intersect each other or meet at is referred to as the centroid of the triangle.

The diagram shows a triangle with three medians that meets at point D in the triangle. Therefore, point D is the centroid of the tringle because lines A.F, BC, and CE are all medians of the given triangle.

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The proper test statistic has a value of 13.21.

As a result, repeated measurements of cholesterol levels from the same blood sample are taken to assess a lab technician's consistency.

The desired accuracy is a measurement variance of 2.78 or less. In the event that the lab technician conducts 16 measurements, and the sample's measurement variance is 2.45.

1) n=16 samples were used.

The desired accuracy is a measurement variance of 2.78 or less.

The sample's measurements' variance is 2.45 or less.

We list both the null and alternative hypotheses in response to the query.

Null hypothesis [tex]H_{0}[/tex] = [tex]var^{2} \geq[/tex]  2.78

Alternative hypothesis [tex]H_{a}[/tex] = [tex]var^{2} <[/tex]  2.78

We claim the alternative hypothesis.

2)Calculate the appropriate test statistic's value.

Using Chi-square,

X= ((n-1)(2.45)/(2.78)

X= 15(2.45)/(2.78)

X=36.75/2.78

X= 13.21

Therefore, The value of the appropriate test statistic is 13.21

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A Stem and Leaf Plot is a special table where each data value is split into a "stem" (the first digit or digits) and a "leaf" (usually the last digit).

With this in mind we conclude that:

There are 8 values in the data set which are greater than or equal to 20 and less than or equal to 29. This comes from the fact that we have to count how many leafs are in the stem 2.

There are 6 values in the data set which are greater than or equal to 10 and less than or equal to 19. This comes from the fact that we have to count how many leafs are in the stem 1.

There are 14 values in the data set which are greater than or equal to 40 and less than or equal to 49. This comes from the fact that we have to count how many leafs are in the stem 4.

Answer:

32x – 72

OR

–72 + 32x

Step-by-step explanation:

To use the Distributive Property, just simply follow my steps:

Write the equation:

–8(9 – 4x)

To distribute, multiply the numbers inside the parenthesis by the number outside of the parenthesis SEPARATELY. It should look like this:

(–8 • 9)(–8 • –4x)

(–72)(32x)

Since the 32 is positive, the equation could be written either way:

–72 + 32x

OR

32x – 72

If you want the equation to be fully solved...

Set the equation equal to zero:

32x – 72 = 0

Isolate the variable. Subtract 72 from both sides:

32x – 72 + 72 = 0 + 72

32x = 0 + 72

32x = 72

Divide:

32x/32 = 72/32

x = 9/4 (Improper Fraction Form)

OR

x = 2 (and) 1/4 (Mixed Number Form)

Convert 9/4 to a decimal:

x = 9/4

x = 2.25

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If two angles be 10x + 5 and 15x - 30 then the value of x = 7.

Let the two angles be 10x + 5 and 15x - 30.

simplifying the above two equations, we get

10x + 5 = 15x - 30

Subtract 5 from both sides

10x + 5 - 5 = 15x - 30 - 5

Simplifying the above equations,

10x = 15x - 35

Subtract 15x from both sides of the equation

10x - 15x = 15x - 35 - 15x

Simplifying the above equation, we get

-5x = -35

Divide both sides by -5

[tex]$\frac{-5 x}{-5}=\frac{-35}{-5}[/tex]

x = 7

Therefore, the value of x = 7.

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Answer:

D. Negative

Step-by-step explanation:

Always read the graph from left to right

The graph is going down thus it is negative

Answer: Negative.

Step-by-step explanation: The graph of the line falls from left to right which makes it negative.

The factors of the given monomial are given below

What is a monomial?

A monomial is, broadly speaking, a polynomial with just one term in mathematics. There are two definitions of a monomial: A monomial, often known as a power product, is a product of powers of variables with nonnegative integer exponents, or a product of variables with repeats. The constant 1 is a monomial, which means that it is equivalent to the empty product and to for any variable x. If just one variable, x, is examined, a monomial is either 1 or a power xn of x, where n is a positive integer. If many variables, say x,y,z, are examined, each can be assigned an exponent, such that each monomial has the form xaybzc with a,b,c non-negative integers.

The factors of the monomial 16x²y are 2.2.2.2.x.x.y

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The factors of the monomial are given below

What is a monomial?

A monomial is, broadly speaking, a polynomial with just one term in mathematics. there are two definitions of a monomial: A monomial, often known as a power product, is a product of powers of variables with nonnegative integer exponents, or a product of variables with repeats. The constant 1 is a monomial, which means that it is equivalent to the empty product and to for any variables x. If just one variable, x, is examined, a monomial is either 1 or a power xn of x, where n is a positive integer, if many variables, say x, y, z, are examined, each can be assigned an exponent, such that each monomial has the form xaybzc with a, b, c non-negative integers.

The factors of the monomial 16x²y are 2.2.2.2.x.x.y

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Answer: 48 ft

Step-by-step explanation:

The height gap between the balloons is 60 -40 = 20 feet. That gap is being closed at the rate of 2 + 3 = 5 ft/s, so will be gone in ...

 (20 ft)/(5 ft/s) = 4 s

At that time, the red balloon will have risen (2 ft/s)(4 s) = 8 ft to a height of ...

 40 ft +8 ft = 48 ft

The blue balloon will have descended (3 ft/s)(4 s) = 12 ft to a height of ...

 60 ft -12 ft = 48 ft

The balloons at at 48 ft when they are both the same height.

_____

Time and speed and distance are related by the formula you see on every speed limit sign:

 speed = distance/time . . . . . . . (on the sign, it's "miles per hour")

or

 time = distance/speed

or

 distance = speed × time

_____

If you want equations, you can write them as ...

 h = 40 +2t

 h = 60 -3t

where h is the altitude the balloons have when they are at the same height, and t is the number of seconds it takes to get there.

We're only interested in h, so we can cancel t by multiplying the first equation by 3 and adding that to the second equation multiplied by 2:

 3(h) + 2(h) = 3(40 +2t) +2(60 -3t)

 5h = 120 +6t +120 -6t

 h = 240/5 = 48 . . . . the height in feet at which the balloons are the same height

Answer:

p(-1) = 7

p(2) = -2

Step-by-step explanation:

We have p(x) = 4 - 3x

p(-1) = 4 - 3(-1) = 4 + 3 = 7

p(2) = 4 - 3(2) = 4 - 6 = -2

Answer: The slope is -0.7, the rise is -1.4, and the run is 2

Answer:

C (0,3)

Step-by-step explanation:

Plot the two equations and the points.  See the attached graph.  The blue area reflects the inequality of y+3x<=8:  many points satisfy this equation and they are all blue.

The red line is equation y-3=x.  There is only one point on this line that is also in the blue area:  (0.3).  The other three points (A, B, and D) do not satisfy either equation.  The metric term for them is losers.

Answer: Well, yes. It's more like p = s + s + s + s. "S" = side. "P" = perimeter.

So, this is theoretically true if your variable for a side just happened to be "n".

You also put, "The perimeter of a square", A simpler way to put this is

P = s4   or in your case P = n4.

Because this shape is a square all side lengths and angles will be congruent, and therefore will all be the same (which is why we are able to multiply one side by four.)

Hope this helps. :)

Answer:

6

Step-by-step explanation:

Trust

Answer: I'm not sure what your options are, but a line the passes through -3,1, and is parallel to y=4, would be y=1

Step-by-step explanation:

the number of sales by b must be 150 to make the same amount of salesman B.

What is Algebraic expression ?

Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.

given that :

Salesman A gets paid $300 a month plus $8 for every sale he makes :

let the no. of sales A made be : x

then, in order to make the same amount of salesman b we equate btoth the amount :

300 + 8x = 1500

8x = 1500-300

8x = 1200

x = 1200/8

x = 150

Therefore, the number of sales by A must be 150 to make the same amount of salesman b.

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Answer:

  20 cm

Step-by-step explanation:

Given a prism with a right triangle base and a volume of 480 cm³, you want the height of the prism. The base has one side 8 cm, and hypotenuse 10 cm.

The missing edge of the right triangle base can be found using the Pythagorean theorem. It tells us the square of the hypotenuse is the sum of the squares of the other two sides:

  b² = c² +a²

  10² = 8² +a² . . . . . . . use given lengths

  a² = 100 -64 = 36 . . . . subtract 8², simplify

  a = 6 . . . . . . . . . . . . . length of side BC

The area of the right triangle base is ...

  A = 1/2bh . . . . . . . . b is the triangle base; h is its height

  A = 1/2(6 cm)(8 cm) = 24 cm²

The volume of the prism is ...

  V = Bh . . . . . . . . . . . . . . . where B is the base area, and h is the height

  480 cm³ = (24 cm²)h . . . use known values

  h = 20 cm . . . . . . . divide by the coefficient of h

The height of the prism is 20 cm.

EXPLANATION

Replacing the given functions into the following:

Removing the parentheses and simplifying:

Simplifying like terms:

Hence,

Yes, you are right!

First of all, we will subtract [tex]5[/tex] from each side.

Then we multiply both sides by [tex]4[/tex].

Then add [tex]3[/tex] to each side.

Finally, we divide each side by [tex]2[/tex].

[tex]\boldsymbol{\sf{\cfrac{2x-3}{4}+5=10 }}[/tex]

Multiply the two sides of the equation by 4.

2x - 3+20 = 40

Add −3 and 20 to get 17.

2x+17 = 40

It remains 17 on both sides.

2x = 40−17

Subtract 17 of 40 to get 23.

2x = 23

Divide both sides by 2.

[tex]\boldsymbol{\sf{x=\dfrac{23}{2} \ \ \longmapsto \ Answer }}[/tex]

We paint with:

• red the regions where the function is decreasing,

• green the regions where the function is increasing.

From the graph, we see that the function is:

• decreasing in the intervals (-∞, -1.5) and (2, ∞),

• increasing in the interval (-1.5, 2).

Answer

• Increasing on the interval(s): ,(-∞, -1.5), (2, ∞)

• Decreasing on the interval(s): ,(-1.5, 2)

Solution

The question would like us to evaluate the following expression

- We should deal with the modulus and bracket separately.

- After that, we can then perform the subtraction operation on the results of the modulus and bracket.

- This is done below:

Also,

Thus, combining both results, we have:

Final Answer

The answer is -6

Answer:

-6 hope it helps

thank you

Volume of a cone is given by;

From the queston,

h = 414

diameter = 416, this implies r = d/2 = 416/2 = 208

π = 3.14

substitute the values into the formula

We want to know what's the probability of spinning a number greater than two

There are 2 spinnings greater than two, of a total of 8. therefore, the probability I will be

The probability is 1/4

Answer:

y > -1

Step-by-step explanation:

8y+9 > 1

   -9    -9

8y > -8

/8    /8

y > -1

The given situation can be solved using the differential equation and the top of the ladder slides downward at 0.417 ft/s.

Let:

x be  the distance from the bottom of the ladder to the base of the wall

y  be the distance from the top of the ladder to the bottom of the wall

When the ladder is still, apply the Pythagorean Theorem,

x² + y² = 13²

5² + y² = 13²

y² = 169 - 25 = 144

y = 12 ft

When the ladder slides, apply the differential equation:

x² + y² = 13²

2x . dx/dt + 2y . dy/dt = 0

Substitute x = 5, dx/dt = 1, y = 12

2 . 5 . 1 + 2 . 12 . dy/dt = 0

24 dy/dt = -10

dy/dt = -5/12 = - 0.417 ft/s

The minus sign indicates that the ladder is sliding downward.

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The value of i where remainder of n/ 4 is 2 is :

i² = -1 .

i² = -1

i⁰ = 1

i¹ = i

i² = -1

i³ = i² x i

  = -1 x i

  = -i

i⁴ = i² x i²

   = -1 x -1

   = 1

The pattern repeats.

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Answer:

10 : 0.02 (20m)