y=0.75(1.05)t Determine whether the function represents a exponential growth or decay.Identify the percent rate of change

Answer:

163,380.48

Step-by-step explanation:

First find the average of the first 4 months' figures.

To do this, find the sum of the first 4 values and then divide by 4, the number of data points:

(14889.51+22936+9856.88+6777.77)/4 = 54460.16/4 = 13615.04

It costs on average £13615.04 per month to run the arena.

This means the estimated running costs for 12 months will be

13615.04(4) = £163,380.48

The statement "If [tex]\( A \subset B \)[/tex], then [tex]\( A \cap B = A \cup B \)[/tex]" is not always true; it holds only if A = B.

The statement "If [tex]\( A \subset B \)[/tex], then [tex]\( A \cap B = A \cup B \)[/tex]" is not always true.

If [tex]\( A \subset B \)[/tex], it means that every element in set A is also in set B.

Now, consider the intersection of A and B [tex](\( A \cap B \))[/tex]. This intersection contains all elements that are common to both sets A and B.

On the other hand, the union of A and B [tex](\( A \cup B \))[/tex] contains all elements that are in either set A or set B, or both.

Since A is a subset of B, all elements in A are already in B, which means [tex]\( A \cap B = A \)[/tex]. However, [tex]\( A \cup B \)[/tex] would just be B, because all elements in A are also in B, so [tex]\( A \cup B \)[/tex] is simply B.

Therefore, the statement "If [tex]\( A \subset B \)[/tex], then [tex]\( A \cap B = A \cup B \)[/tex]" is not true in general; it is true only if A = B .

Answer:  The total number of fifth graders in the school is 155.

Step-by-step explanation:  Given that at Brown Elementary School, 80% of all fifth graders ride the bus to school.

If 124 fifth graders ride the bus to school, we are to find the number of fifth graders in the the school.

Let, 'n' be the total number of fifth graders in the school.

Then, according to the given information, we have

[tex]80\%\times n=124\\\\\\\Rightarrow \dfrac{80}{100}\times n=124\\\\\\\Rightarrow \dfrac{4}{5}n=124\\\\\\\Rightarrow n=\dfrac{124\times 5}{4}\\\\\\\Rightarrow n=31\times5\\\\\Rightarrow n=155.[/tex]

Thus, the total number of fifth graders in the school is 155.

We can convert inches to meters with the following conversion formula:

1 inch = 0.0254 meters

Now we have to find how many meters are there in 276 inches.

So multiplying 0.0254 with 276 would give us the answer.

276 inches = 0.0254 *276 = 7.0104 meters.

Answer : There are 7.0104 meters in 276 inches.

The coordinates of point Q are (-10, 10, 4).

To find the coordinates of point Q, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint between two points P(x1, y1, z1) and Q(x2, y2, z2) are given by the average of the coordinates:

R = ((x1 + x2) / 2, (y1 + y2) / 2, (z1 + z2) / 2)

In this case, we are given that the midpoint R has coordinates (-3, 2, -1) and one of the points P has coordinates (4, -6, -6). Plugging in these values into the midpoint formula, we can solve for the coordinates of point Q:

Q = (2 * R - P)

Q = (2 * (-3, 2, -1) - (4, -6, -6))

Q = (-6, 4, -2) - (4, -6, -6)

Q = (-10, 10, 4)

we know that

To find out the fraction of a pan of brownies that was left subtract [tex]1\frac{1}{5}[/tex] from [tex]2[/tex]

remember that

[tex]1\frac{1}{5}=(1*5+1)/5=\frac{6}{5}[/tex]

so

[tex]2-\frac{6}{5} =(2*5-6)/5=\frac{4}{5}[/tex]

therefore

the answer is

the fraction of a pan of brownies that was left is [tex]\frac{4}{5}[/tex]

The length in feet of the metal frame that surrounds the trampoline is 44 ft.

The circumference of a circle is the distance round the circle.

The circumference of a circle = πD

3.14 x 14 = 44 ft

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The equivalent fractions with the same denominator are 6/ 15 and 5 /15.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the two fractions are 2/5 and 1/3. The two equivalent expressions with the common base will be written as:-

2/5 = ( 2 x 3 ) / ( 5 x 3 )

2//5 = 6 / 15

1/3 = ( 1 x 5 ) / ( 3 x 5 )

1 / 3 = 5 / 15

Therefore, the two fractions are 6/ 15 and 5 /15.

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The expression that shows identity property of multiplication is (x+yi)×1=(x+yi), the correct option is D.

According to the identity property of multiplication, the product of 1 and a number is the number itself.

The expressions in the question are

(X+yi)×z=(xz+yzi)

(x+yi)×0=0

(x+yi)×(z+wi)=(z+wi)×(x+yi)

(x+yi)×1=(x+yi)

The only expression that shows this property is (x+yi)×1=(x+yi).

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Answer:

sample response:  None of the roots can have multiplicity because the polynomial is cubic and 3 roots are given. Write each root as a linear factor, then multiply the three factors to get the expression for the function.

Step-by-step explanation:

Answer:

The Edg answer is as follows -

The statement is not true for all real numbers. It is only true for decimal or fractional values of x .

If x is an integer, then the ceiling function returns x when the input is x . But, the flooring function returns x + 1 when the input is x + 1.

Since x does not equal x + 1 when x is an integer, the expressions are not equal when x is an integer.

Step-by-step explanation:

Real numbers are set of numbers that include rational and irrational numbers.

[x]=[x+1] is not true for all real numbers

Assume that: x is an integer

And x = 5

So, the equation becomes

[tex]5 = 5 + 1[/tex]

[tex]5 = 6[/tex]

The above equation is not true, because:

[tex]5 \ne 6[/tex]

Hence, [x]=[x+1] is not true for all real numbers

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The circumference and the area of the circular bed are 14π feet = 43.9823 feet and 49π feet² = 153.9380 feet² respectively.

The circumference is the total length covered by the boundary of an object.

To calculate the circumference of a circle with radius r units, we use the formula: Circumference = 2πr units.

The area of an object is the space its planar face or two-dimensional face covers.

To calculate the area of a circle of radius r units, we use the formula: Area = πr² sq. units.

In the question, we are asked to find the circumference and the area of the circular flower bed that a gardener makes, having a diameter of fourteen feet.

We know that radius = diameter/2 = 14/2 = 7 feet.

To calculate the circumference of the circular bed, we will use the formula 2πr, where r is the radius.

Substituting the radius, r = 7 feet in the above formula, we get:

Circumference = 2(π)(7) feet = 14π feet = 43.9823 feet.

To calculate the area of the circular bed, we will use the formula πr², where r is the radius.

Substituting the radius, r = 7 feet in the above formula, we get:

Area = (π)(7)² feet² = 49π feet² = 153.9380 feet².

Thus, the circumference and the area of the circular bed are 14π feet = 43.9823 feet and 49π feet² = 153.9380 feet² respectively.

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Jensen stopped at A and planned to stop at B next. He has a map with a scale of 1 inch to 35 miles.

It is clear that 1 inch on map corresponds to 35 miles in actual.

From the map he has, we can see that both places A and B are 2.5 inches apart on map.

Let's assume those are "X" miles away in actual. Then we can use proportions to solve this problem.

1 inch to 35 miles would be same as 2.5 inches to X miles. Mathematically, we can write it as follows :-

[tex] \frac{1 \;inch}{35 \;miles} =\frac{2.5 \;inches}{X \;miles} \\\\
\frac{X \;miles}{35 \;miles} =\frac{2.5 \;inches}{1 \; inch} \\\\
\frac{X}{35} =\frac{2.5}{1} \\\\
Cross \;\;multiplying \\\\
X = 35*2.5=87.5 \;miles [/tex]

Hence, actual distance between A and B is 87.5 miles.

Final answer:

The surface area of a right rectangular prism with dimensions of 6cm by 14cm by 5cm is calculated by summing up the areas of all faces, resulting in a total surface area of 368cm².

Explanation:

To calculate the surface area of a right rectangular prism, we need to find the area of all the faces and add them together. For a prism with dimensions of 6cm by 14cm by 5cm, it has three pairs of identical faces: two faces that are 6cm by 14cm, two faces that are 6cm by 5cm, and two faces that are 14cm by 5cm.

Using the area formula for rectangles (Area = length × width), we find the areas of these faces:

For the 6cm by 14cm faces: Area = 6cm × 14cm = 84cm². Since there are two such faces, their combined area is 2 × 84cm² = 168cm².

For the 6cm by 5cm faces: Area = 6cm × 5cm = 30cm². Since there are two such faces, their combined area is 2 × 30cm² = 60cm².

For the 14cm by 5cm faces: Area = 14cm × 5cm = 70cm². Since there are two such faces, their combined area is 2 × 70cm² = 140cm².

Adding up all these areas gives us the total surface area of the prism:

Total Surface Area = 168cm² + 60cm² + 140cm² = 368cm²

Therefore, the surface area of the right rectangular prism is 368cm².

The answer is:

5 hours, 246 miles.

Since we know the equations that represent the distances of both cars at certain times (function of time), we can calculate the time that they will be at the same distance by making their equation equal.

So, we are given the equations:

A-

[tex]y=44x+26[/tex]

B -

[tex]y=36x+66[/tex]

Now, by making both equation equal, we can calculate the time that they will have the same distance, so, we have:

[tex]44x+26=36x+66[/tex]

[tex]44x-36x=66-26[/tex]

[tex]8x=40[/tex]

[tex]x=\frac{40}{8}=5[/tex]

Hence, we have that they will have the same position after 5 hours.

Then, to calculate the distance, we need to substitute the obtained time in any of the given equations, so, substituting into A, we have:

[tex]y=44x+26[/tex]

[tex]y=44*5+26=220+26=246[/tex]

We have that the distance will be 246 miles.

Hence, we have that the answer is:

5 hours, 246 miles.

Have a nice day!

I think its both because An arithmetic sequence is a sequence of numbers in which the difference between any two consecutive terms is constant. Consecutive means one after the other. The constant value is called the common difference. Another way to think about an arithmetic sequence is that each term in the sequence is equal to the previous term plus the common difference and also A geometric sequence is a sequence in which the ratio of any two consecutive terms is constant. This constant value is called the common ratio. Another way to think about a geometric sequence is that each term is equal to the previous term times the common ratio. So when u look at it check out if the 16, 8, 4, and 2 see if they fit these terms

The ratios are constant (0.5), so the sequence is geometric.

Since the sequence is not arithmetic but is geometric, the correct answer is: B. Geometric

To determine whether the sequence 16, 8, 4, 2 is arithmetic, geometric, both, or neither, let's analyze the differences between consecutive terms and the ratios between consecutive terms.

Arithmetic Sequence:

An arithmetic sequence is a sequence in which the difference between consecutive terms is constant.

Calculating the differences:

8 - 16 = -8

4 - 8 = -4

2 - 4 = -2

The differences are not constant, so the sequence is not arithmetic.

Geometric Sequence:

A geometric sequence is a sequence in which the ratio between consecutive terms is constant.

Calculating the ratios:

8 / 16 = 0.5

4 / 8 = 0.5

2 / 4 = 0.5

The ratios are constant (0.5), so the sequence is geometric.

Since the sequence is not arithmetic but is geometric, the correct answer is:

B. Geometric

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It says to check if [tex] \frac{3}{8} [/tex] satisfy each equation or not.

Checking first equation :-

96 x [tex] \frac{3}{8} [/tex]

⇒ [tex] \frac{96 * 3}{8} [/tex]

⇒ [tex] \frac{288}{8} [/tex] = 36

⇒ 36 = 36. First equation is "YES".

Checking second equation :-

38 x [tex] \frac{3}{8} [/tex]

⇒ [tex] \frac{38 * 3}{8} [/tex]

⇒ [tex] \frac{114}{8} [/tex] = [tex] \frac{57}{4} [/tex]

⇒ [tex] \frac{57}{4} [/tex] ≠ 14. Second equation is "NO".

Checking third equation :-

16 x [tex] \frac{3}{8} [/tex]

⇒ [tex] \frac{16 * 3}{8} [/tex]

⇒ [tex] \frac{48}{8} [/tex] = 6

⇒ 6 = 6. Third equation is "YES".

Checking fourth equation :-

56 x [tex] \frac{3}{8} [/tex]

⇒ [tex] \frac{56 * 3}{8} [/tex]

⇒ [tex] \frac{168}{8} [/tex] = 21

⇒ 21 = 21. Fourth equation is "YES".