What is the range of the data below?
A: 22
B: 28
C: 41
D: 42

Option c is correct-  To demonstrate the existence of a cause-and-effect relationship between two variables.

The goal of experimental research study is different from the goal of non experimental research. The experiment attempts to show the change in one variable due to change in another variable.

The goal of the experimental method is to provide more definitive conclusions about the causal relationships among the variables in a research hypothesis than what is available from correlational research.

To accomplish this goal the an experiment control extraneous variables and manipulate independent variables. The experiment is done by changing one variable by manipulating which causes change in another variable. The researcher must control the research situation.

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Using simple interest, the amounts she invested are given as follows:

Simple interest is used when there is a single compounding per time period, usually measured in years.

The amount of money after t periods in is modeled by:

A(t) = P(1 + rt)

The interest accrued after t periods is modeled by:

I(t) = Prt

In which:

She had two investments, investing a total of $4500, hence:

\(P_1 + P_2 = 4500\)

The return for the 9% investment exceeds that from the 6% investment by $180, hence:

Then:

\(I_2 = 0.06(4500 - P_1)\)

\(I_1 - 180 = 0.06(4500 - P_1)\)

\(0.09P_1 - 180 = 0.06(4500 - P_1)\)

\(0.15P_1 = 450\)

\(P_1 = \frac{450}{0.15}\)

\(P_1 = 3000\)

Which is the amount invested at 9%, hence the amount invested at 6%, considering that a total of $4,500 was invested, is given by:

4500 - 3000 = $1,500.

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Answer:

If y and x have a proportional relationship, then we can write an equation of the form y = kx, where k is a constant of proportionality.

To find the value of k, we can use the given values of y and x:

y = kx

24 = k(12)

k = 2

Now that we know k, we can use the equation to find the value of y when x=16:

y = kx

y = 2(16)

y = 32

Therefore, when x=16, y=32.

Answer:

Let's say you sold some goods to a customer. If the customer is not satisfied with the goods and returns it back to you, then it is called sales return.

Answer: 12

Step-by-step explanation:

An angle is a mathematical term which we can defined, when two straight lines or rays meets at a common endpoint. The common point is called the vertex of an angle. The word angle comes from a Latin word named ‘angulus,’.

Interior angles:- The  inner angle made by the intersection of two polygonal sides.

Exterior angles:-  The  outer angle made by the intersection of two polygonal sides.

Given that,

All the exterior angles are,

(5x + 4), (7x + 4),(4x + 9),(4x + 1),(9x-6)

It is known that,

Sum of Interior angle & Exterior angle is equal to 180°

So we can calculate all the Interior angles,

180°- (5x + 4),  180°-(7x + 4),   180°-(4x + 9),   180°-(4x + 1),    180°-(9x-6)

Formula for sum of all the Interior angles = (2n-4)×90

So, n=5

Sum of all the Interior angles = 540°

[180°- (5x + 4)] + [180°-(7x + 4)]+[180°-(4x + 9)]+[180°-(4x + 1)] +[180°-(9x-6)] = 540

900- 29x- 12 = 540

x = 12

Hence, The value of x is, 12

The reasonable domain for the function f(x) = -2/3x + 4 in this situation is B. 0 ≤ x ≤ 6

In this question, we have:

Function, f(x) = -2/3x + 4

Where

x is the bottles of hand sanitizer per month

The function f(x) cannot be less than 0

So, we have

-2/3x + 4 = 0

This gives

-2/3x = -4

Solve for x

x = 6

This means that x cannot exceed 6

Hence, the domain is (b) . 0 ≤ x ≤ 6

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The overall reaction ordering affects the units of the rate constant, k. M/s, 1/s, and 1/(Ms) are the units of k for a zero-order reaction, first-order reaction, and second-order reaction, respectively.

The unit of the rate constant is the same as the unit of reaction rate for zero-order reactions. It is either sM or Lsmol. The unit of rate constant for a first-order reaction is s-1 or min-1. The rate constant for a reaction of order 1 is expressed in units of s-1. The rate constant for a reaction of order 2 is measured in M-1 s-1 (or) L mol-1 s-1. M1-n s-1 (or L(-1+n) mol(1-n) s-1) is the unit of rate constant for reactions with order n.

The following is the rate law's mathematical formulation.

Rate = K(A)m(B)n

The link between the rate of a chemical reaction and the concentration of reactants is shown by this rate law.

In the above equation, the reactant molar concentrations are [A] and [B], respectively, and the rate constant K is used.

The value of K is particular to a given reaction at a given temperature. Experiments were used to determine the represent exponents m and n. The value of K depends on surface area and temperature rather than reactant concentrations.

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The augmented matrix corresponding to the system of equations in this problem is given as follows:

[-6 -5 -4 7].

[7 -9 -1 -7].

[-9 -3 -6 7].

The first row is constructed according to the coefficients of the first equation, hence it is given as follows:

[-6 -5 -4 7].

The second row is constructed according to the coefficients of the second equation, hence it is given as follows:

[7 -9 -1 -7].

The third row is constructed according to the coefficients of the third equation, hence it is given as follows:

[-9 -3 -6 7].

Hence the matrix is given as follows:

[-6 -5 -4 7].

[7 -9 -1 -7].

[-9 -3 -6 7].

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The range of the equation f(x) = 3ˣ ⁻ ¹ - 2 is  y > -2

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

f(x) = 3ˣ ⁻ ¹ - 2

The above equation is an exponential function

The rule of an exponential function is that

In this case, it is -2

So, the range is y > -2

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The surface area of the pyramid is 113 cm².

A rectangular pyramid is a type of pyramid where the base is a rectangle and the triangular faces meet at a single point called the apex or vertex. It has five faces, including a rectangular base and four triangular faces, and it is a polyhedron with five vertices and eight edges.

The rectangular pyramid has a base of dimensions 7 cm by 5 cm, and the two large triangular faces have a height of 7.6 cm, while the two small triangular faces have a height of 8 cm.

To find the surface area of the pyramid, we need to find the area of each face and then add them up.

Area of the base:

The base of the pyramid is a rectangle with dimensions 7 cm by 5 cm, so its area is:

Area of base = length × width = 7 cm × 5 cm = 35 cm²

Area of the four triangular faces:

Each of the four triangular faces has a base of 5 cm (the width of the rectangle) and a height of either 7.6 cm or 8 cm. Using the formula for the area of a triangle, we can find the area of each face:

Area of each large triangular face = 1/2 × base × height = 1/2 × 5 cm × 7.6 cm = 19 cm²

Area of each small triangular face = 1/2 × base × height = 1/2 × 5 cm × 8 cm = 20 cm²

There are two large triangular faces and two small triangular faces, so the total area of the four triangular faces is:

Total area of four triangular faces = 2 × area of large triangular face + 2 × area of small triangular face

= 2 × 19 cm² + 2 × 20 cm²

= 78 cm²

Total surface area:

Finally, we can find the total surface area of the pyramid by adding the area of the base to the total area of the four triangular faces:

Total surface area = area of base + total area of four triangular faces

= 35 cm² + 78 cm²

= 113 cm²

Therefore, the surface area of the pyramid is 113 cm²

.

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Answer:

X will equal 10 x=10

Step-by-step explanation:

First subtract 100 from both sides to get x^2-20x=-100 then find c. (-b/2)^2 is the formula. then c=100 so add 100 to both sides. x^2-20x+100=200. Then Factor. (x-10)^2=0 is what you should get. then do square root. x-10=0. So now add 10 to both sides and you get x=10. Tada!

Answer:

x = 35

Step-by-step explanation:

since the figures are similar then the ratios of corresponding parts are in proportion, that is

\(\frac{x}{10}\) = \(\frac{14}{4}\) = \(\frac{7}{2}\) ( cross- multiply )

2x = 7 × 10 = 70 ( divide both sides by 2 )

x = 35

As Tan A=Perpendicular/Base, x has the value of 21.56. Tan 54 = x/32, or x = 21.56, in this case.

When two lines cross at a 90-degree angle, they are said to be perpendicular. The definition of a parallel line is a line with constant spacing. being perfectly vertical or upright: making a straight angle with one another or another given line or plane. Adverbial phrase meaning "perpendicularly"

As a result of two lines meeting at a right angle, the word "perpendicular" denotes "at right angles." Including up and down, across, and side to side, perpendicular lines can face in any direction. Additionally, they don't need to be standing straight up from the bottom or side of the page.

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The least common denominator needed to solve the equation is given as follows:

D. x(x - 3).

The equation in this problem is given as follows:

1/x + 2/(x - 3) = 5.

The denominators of each expression are given as follows:

x and x - 3 are not factors of each other, hence we multiply them and the least common denominator needed to solve the equation is given as follows:

D. x(x - 3).

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Answer:

Option D.   \(g(x)=5(0.8)^{x}+2\)

Step-by-step explanation:

Main concepts

Concept 1: identifying horizontal asymptote

Concept 2: assuring decreasing exponential function

Concept 1. identifying horizontal asymptote

Any exponential function of the form \(y=a*b^x\) has a horizontal asymptote on the x-axis.  A constant (positive or negative) added to the end of the exponential expression will shift the graph of the exponential function up (if positive) or down (if negative) the number of units equal to the magnitude of the number.  Since the original function f(x) has a "+2" at the end, it has been shifted up 2 units.  Thus, we can eliminate answers A and C from feasible answers since they each shift the exponential function up 3 units, not 2.

Concept 2. assuring decreasing exponential function

Exponential functions of the form \(y=a*b^x\) increase or decrease based on the value of "b".

Observe that the graph of the function f(x) is decreasing, and the value of b=0.5.

To ensure that g(x) also decreases, the b-value must be between 0 and 1, which eliminates option B.

Option D is the correct answer because the value of "b" is between 0 and 1 (making the graph of the function a decreasing exponential), and the number added at the end is "+2", causing the horizontal asymptote to be at a height of positive 2.

Answer:

Since this is a proportional relationship,

We know that the number which are proportional are a multiple of each other

the number which we can multiply one of the numbers to get the other number is the constant of proportionality

we could check for proportionality by using the following formula:

p1 / s1 = p2/s2 = p3/s3 = p4/s4  if they were equal, we can say that the relation is proportional

The value of any of the above values, p1/s1 , p2/s2 , p3/s3 , p4/s4 is the constant of proportionality

Therefore, the constant of proportionality = 20 / 5 = 4

Answer:

Since this is a proportional relationship,

We know that the number which are proportional are a multiple of each other

the number which we can multiply one of the numbers to get the other number is the constant of proportionality

we could check for proportionality by using the following formula:

p1 / s1 = p2/s2 = p3/s3 = p4/s4  if they were equal, we can say that the relation is proportional

The value of any of the above values, p1/s1 , p2/s2 , p3/s3 , p4/s4 is the constant of proportionality

Therefore, the constant of proportionality = 20 / 5 = 4

Answer:

Jessica (23,450 stickers)

The initial temperature of the soda is 22 degrees Celsius, and its temperature after 20 minutes is approximately 10 degrees Celsius.

To find the initial temperature of the soda, we need to evaluate the temperature function T(x) at x = 0.

T(x) = -5 + 27e^(-0.03x)

T(0) = -5 + 27e^(-0.03(0))

T(0) = -5 + 27e^0

Since any number raised to the power of 0 is 1, we have:

T(0) = -5 + 27(1)

T(0) = -5 + 27

T(0) = 22

Therefore, the initial temperature of the soda is 22 degrees Celsius.

To find the temperature of the soda after 20 minutes, we evaluate the temperature function at x = 20.

T(x) = -5 + 27e^(-0.03x)

T(20) = -5 + 27e^(-0.03(20))

T(20) = -5 + 27e^(-0.6)

Using a calculator, we can compute e^(-0.6) ≈ 0.5488.

T(20) = -5 + 27(0.5488)

T(20) = -5 + 14.8152

T(20) ≈ 9.8152

Therefore, the temperature of the soda after 20 minutes is approximately 10 degrees Celsius (rounded to the nearest degree).

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Answer:

me too (help)

Step-by-step explanation:

By solving for x you get x=6

Answer:

x = 6

Step-by-step explanation:

12x = 72

72/12 = 6

x = 6

Answer:

2x

Step-by-step explanation:

5, 10, 20, 40, 80

each step is multiplying by 2, therefore the sequence is 2x

Answer:

t=6

Step-by-step explanation:

They could go for 6 hours as 6x5=35 and the $14 fee is 49 so it would be 5(6)+14=49 when t=6

hope this helps

The length of AB and CB is 7√2.

Using Trigonometry

cos 45 = B/ H

cos 45 = AD / AB

1/√2 = 7 / H

H = 7√2

Then, CB = AB = 7√2

Now, using Pythagoras theorem in ΔABC

AC² = AB² + CB²

14² =  (7√2)² + CB²

CB² = 196 - 98

CB = 7√2

Thus, the length of AB and CB is 7√2.

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The dimension of the rectangular of a norman window will be 1.6803*3.3606.

What is the area of Rectangle?

In any quadrilateral which have equal and parallel opposite sides is considered to be a rectangle. It is also called as a polygon with four sides and the four angles that are all 90 degrees each. A rectangle is a shape with only two dimensions. The product of the length and the breadth calculates its area. The length of the diagonals of any rectangle are equal in length. Thus, the length of the diagonals can be calculated easily using the Pythagoras theorem where, the diagonal is considered to be the hypotenuse.

Let r represents the radius, and b be the breadth.

Then, perimeter = 3.14*r+2r+2b = 12

For the dimension needed for the most light to enter we need to maximize the area.

Hence, area of the window : area of the semicircle + area of the rectangle

= \(\frac{3.14*r^2}{2} + 2rb\)

= \(12r - (\frac{3.14+4}{2}) r^2\)

A'(r) = 0

Therefore, \(r=\frac{12}{3.14+4}\) which is nearly equal to 1.6803m

From this value of r we can calculate the value of b to be;

b= 1.6803m

Thus, a= 3.606m

Thus the required dimension is : 1.6803*33606

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Answer:

Both.

Step-by-step explanation:

The perimeter of a trapezuun is given by : a + b + c + d ; where a, b, c, d are the lengtb of the sides of the trapezium.

The perimeter of the trapezium Given below is :

(4 + 6 + 4 + w + 2)

Evaluating both expressions :

Peter = 6 + 4 + (w + 2) + 4

Christine's expression = w + 16

From the expression, we can see that Peter's expression is correct s he wrote the sum of all the four sides

As for Christine's expression, it is also right ; as she added all the sides to obtain a reduced term

Hence, both are correct

Answer:

both of them are correct

Step-by-step explanation:

-1-1 or 2-4 or 3-5 or 6-8 or 7-9 or 8-10

Answer:

I honestly don't know man

Step-by-step explanation:

but you can do this you got it

Answer:

The last option is my best guess

Step-by-step explanation:

The amount of solution A and B required are 60 and 90 ounces respectively.

Creating simultaneous equations for the problem:

Mass of solution A = a

Mass of solution B = b

a + b = 150 _____(1)

0.65a + 0.90b = 150×0.80

0.65a + 0.90b = 120 __(2)

From (1)

a = 150-b ____(3)

substitute (3) into (2)

0.65(150-b) + 0.90b = 120

97.5 - 0.65b + 0.90b = 120

0.25b = 120-97.5

0.25b = 22.5

b = 22.5/0.25

b = 90

a = 150 - b

a = 150 - 90

a = 60

Therefore , 60 ounces of solution A and 90 ounces of solution B is required.

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