The scale on a map shows that 2 inches represents 15 miles. Which proportion can be used to find the actual distance, x, represented by 30 inches on the map?

The unit rate for a bagel at Fresh side is $0.09 cheaper than the unit rate at

Value mart for bagels.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, Fresh side grocery sells 7 bagels for $4.41.

∴ The cost of one bagel at Fresh side is $(4.41/7) = $0.63.

Value mart sells 5 bagels for $3.60.

∴ The cost of one bagel at Value mart is

= $(3.60/5).

= $0.72

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Answer:

a = 0.75

b= 0.4375

d= 0.6

e=0.175

f= 2.55

Step-by-step explanation:

By simple division method, the following answers can be calculated:

a.

=[tex]\frac{3}{4}[/tex]

=0.75

b.

= [tex]\frac{7}{16}[/tex]

=0.4375

d.

= [tex]\frac{3}{5}[/tex]

=0.6

e.

= [tex]\frac{7}{40}[/tex]

=0.175

f.

=[tex]\frac{51}{20}[/tex]

=2.55

Thus, the answer are :

a = 0.75

b= 0.4375

d= 0.6

e=0.175

f= 2.55

Answer:

A.0.75 B.0.4375 C. 14.4 D. 0.6 E. 0.175 F. 2.55

Step-by-step explanation:

If Michael has earned $240 interest on an initial investment of $2,000. , then simple interest is 3% for paying in bank.

Simple interest is a quick and easy method of calculating the interest charge on a loan.

Given that,

I = interest = $240

P = principal (investment)=2000

R = simple interest rate=?

T = years= 4 years

Formula: I = PRT

Plug into formula:

240 = 2000(R)4

Multiply right side 2000×4

240 = 8000R

Divide both sides by 8000.

R = 240/8000

R = 0.03

Now multiply with 100

The simple annual interest rate was .03 or 3%.

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The value of 0 to the power of 0 (0^0) is undefined, it may be treated as 1.

The value of 0 raised to the power of 0 (0^0) is undefined.

Mathematically, any nonzero number raised to the power of 0 is equal to 1. However, 0^0 is an indeterminate form, meaning that it does not have a well-defined value.

When evaluating expressions involving 0^0, different contexts may assign different values to it. In some cases, it may be treated as 1, while in others, it may be considered as undefined.

Answer:

B 3 times

C. 4 times

Step-by-step explanation:

For Tristan to  jog between 2 and 3 miles, the number of times he would have to jog the route that is 7/10 mile must be such that the product of the number of times and 7/10 miles gives a number between 2 and 3.

Considering the options given

A. 2 * 7/10 = 1.4 miles (this is not within the range)

B. 3 * 7/10 = 2.1 miles (this is within the range)

C. 4 * 7/10 = 2.8 miles (this is within the range)

D. 5 * 7/10 = 3.5 miles (this is not within the range)

Answer:

The second graph.

Step-by-step explanation:

When the time is 0, the ride has not yet begun.  Therefore the height above ground is nearly nothing.

As time increases, the ride goes up until it hits the top.  The ride then goes back down nearly to the ground.  This is one time around.

The ride then goes back up to the top and back down to the starting point.

This is the motion of the second graph, so the second graph is correct.

The second graph is used to represent A child rides around on a ferris wheel twice.

Graph is a mathematical representation of a network and it describes the relationship between lines and points

In the given graphs, the relationship between the height above ground and times are represented.

The second graph given is best suited to represent "A child rides around on a ferris wheel twice"

When the time is 0, the ride has not yet begun.  Therefore the height above ground is nearly nothing.

As time increases, the ride goes up until it hits the top.  The ride then goes back down nearly to the ground.  This is one time around.

The ride then goes back up to the top and back down to the starting point.

This is the motion of the second graph, so the second graph is correct.

Hence second graph is used to represent the given situation.

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The simplification of the given expression is 0.6i.

Complex numbers are those numbers that contain the imaginary and the real part.

A Complex value z is written in a rectangular form as z = x+iy where (x, y) is the rectangular coordinates.

where r is the modulus of the complex number and θ is the argument

r =√x²+y² and θ = tan⁻¹y/x

Usually the simplification involves proceeding with the pending operations in the expression.

We need to simpify the 0.4i - i

= i(0.4-1)

= 0.6i

Therefore, the simplification of the given expression is 0.6i.

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Answer:

[tex](f-g)(x) = -x^{3} - 3\cdot x + 2[/tex]

Step-by-step explanation:

The new function is:

[tex](f-g) (x) = -3\cdot x + 2 -x^{3}[/tex]

[tex](f-g)(x) = -x^{3} - 3\cdot x + 2[/tex]

The missing x-values are 9, 24, 12, and 16, ensuring proportions remain equal in each ratio set.

To find the missing values that make the sets of ratios equivalent, we can use proportions.

1. Tiles 2 : 3 = 6 : x

  Cross multiplying, we get: 2x = 18

  So, x = 9

2. 4 : 7 = x : 42

  Cross multiplying, we get: 7x = 168

  So, x = 24

3. 2x : 48 = 3 : 12

  Cross multiplying, we get: 12x = 144

  So, x = 12

4. 12 : 15 = x : 20

  Cross multiplying, we get: 15x = 240

  So, x = 16

Therefore, the x-values that make the sets of ratios equivalent are:

1. x = 9

2. x = 24

3. x = 12

4. x = 16

The answer 108 degrees.

Answer: [tex]108^{\circ}[/tex]

Step-by-step explanation:

The sum of all the angles in a regular polygon with sides n , is given by :-

[tex]S_n=180^{\circ}(n-2)[/tex]

Now, the sum of all the angles in a regular pentagon with 5 sides will be :-

[tex]S_5=180^{\circ}(5-2)=180^{\circ}(3)=540^{\circ}[/tex]

We know that all the interior angles of a regular polygon are equal .

Therefore, the measure of each interior angle in a pentagon is given by :-

[tex]x=\dfrac{540^{\circ}}{5}=108^{\circ}[/tex]

Hence, the measure of each interior angle in a pentagon=[tex]108^{\circ}[/tex]

Answer:

Option 1 - Division Property of Equality

Step-by-step explanation:

Given : If  [tex]4x=20[/tex], then x=5.

To find : Which property justifies this statement?

Solution :

The equation is  [tex]4x=20[/tex]

To make variable separate we have to remove 4 which is in multiple of variable x.

So, We divide both side by 4,

Applying division property of equality,

We can divide both sides of an equation by the same number and preserve equality.

[tex]\frac{4x}{4}=\frac{20}{4}[/tex]

[tex]x=5[/tex]

Therefore, The property justifies the statement is 'Division Property of Equality'.

So, Option 1 is correct.

To find the difference in weight between the Newfoundland and the Springer Spaniel, subtract the weight of the Springer Spaniel from the weight of the Newfoundland.

To find the difference in weight between the Newfoundland and the Springer Spaniel, we need to subtract the weight of the Springer Spaniel from the weight of the Newfoundland. The Newfoundland weighs 52 kilograms 656 grams more than a Cocker Spaniel. So, we first need to find the weight of a Cocker Spaniel by subtracting 7,590 grams from the weight of the Springer Spaniel. We then add this weight to the weight of the Newfoundland to get the final answer. Let's calculate:

We can now substitute the given values into these equations and solve.

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A function [tex]f[/tex] from a set [tex]A[/tex] to a set [tex]B[/tex] is a relation that assigns to each element [tex]x[/tex] in the set [tex]A[/tex] exactly one element [tex]y[/tex] in the set [tex]B[/tex]. The set [tex]A[/tex] is the domain (also called the set of inputs) of the function and the set [tex]B[/tex] contains the range (also called the set of outputs).

[tex]We \ denote \ the \ \mathbf{exponential \ function} \ f \ with \ base \ a \ as: \\ \\ f(x)=a^x \\ \\ where \ a>0, \ a\neq 1, \ and \ x \ is \ any \ real \ number[/tex].

We have the following equation:

[tex]y=100(1-12)^t[/tex]

That can be written as:

[tex]y=100(-11)^t[/tex]

Recall that the definition of exponential functions establishes that:

[tex]We \ denote \ the \ \mathbf{exponential \ function} \ f \ with \ base \ a \ as: \\ \\ f(x)=a^x \\ \\ where \ a>0, \ a\neq 1, \ and \ x \ is \ any \ real \ number[/tex].

That is:

[tex]a \ \mathbf{must} \ be \ greater \ than \ 1[/tex]

In this problem, [tex]a=-11[/tex], therefore this is not an exponential function.

The function:

[tex]y=0.1(1.25)^t[/tex]

is an exponential function because is a function of the form [tex]f(t)=ka^t \\ \\ where \ a>0 \ and \ k \ constant[/tex]

So [tex]k=0.1 \ and \ a=1.25[/tex]. Since [tex]a \ is \ greater \ than \ 1[/tex] and being raised to the power of [tex]t[/tex], the function increases. This means that [tex]y[/tex] increases as [tex]t[/tex] increases as illustrated in Figure 1. This represents a growth.

The function:

[tex]y=((1-0.03)12)^{2t}[/tex] can be written as:

[tex]y=11.64^{2t}[/tex]

and is an exponential function because is a function of the form [tex]f(t)=a^{bt} \\ \\ where \ a>0 \ and \ b \ constant[/tex]

So [tex]a=11.64 \ and \ b=2[/tex]. Since [tex]a \ is \ greater \ than \ 1[/tex] and being raised to the power of [tex]2t[/tex], the function increases. As in the previous exercise, this means that [tex]y[/tex] increases as [tex]t[/tex] increases as illustrated in Figure 2. This represents a growth.

The function:

[tex]y=426(0.98)^t[/tex]

is an exponential function because is a function of the form [tex]f(t)=ka^t \\ \\ where \ a>0 \ and \ k \ constant[/tex]

So [tex]k=426 \ and \ a=0.98[/tex]. Since [tex]a \ is \ less \ than \ 1[/tex] and being raised to the power of [tex]t[/tex], the function decreases. Here this means that [tex]y[/tex] decreases as [tex]t[/tex] increases as illustrated in Figure 3. This represents a decay.

The function:

[tex]y=2050(12)^t[/tex]

is an exponential function because is a function of the form [tex]f(t)=ka^t \\ \\ where \ a>0 \ and \ k \ constant[/tex]

So [tex]k=2050 \ and \ a=12[/tex]. Since [tex]a \ is \ greater \ than \ 1[/tex] and being raised to the power of [tex]t[/tex], the function increases. So in this function [tex]y[/tex] also increases as [tex]t[/tex] increases as illustrated in Figure 4. This represents a growth.

Answer:

1. isn't an exponential function

2. growths

3. growths

4. decay

5. growths

Step-by-step explanation:

The exponential functions has the form: y = k1*k2^(k3*t), where k1, k2 and k3 are a constants, and k2>0. Graph of exponential functions always decrease or always increase. To know if a function growths or decay just evaluate the function in 2 points, for example t = 0 and t = 1, and compare their results.

1.

y = 100*(1−12)^x = 100*(−11)^x

Since (-11) is negative, then y is not an exponential function

2.

y(0) = 0.1*(1.25)^(0) = 0.1

y(1) = 0.1*(1.25)^(1) = 0.125

y(1) > y(0) -> growths

3.

y(0) =((1−0.03)12)^2(0) = 1

y(0) =((1−0.03)12)^2(1) = 135.4896

y(1) > y(0) -> growths

4.

y(0) = 426(0.98)^(0) = 426

y(1) = 426(0.98)^(1) = 417.48

y(1) < y(0) -> decay

5.

y(0) = 2050(12)^(0) = 2050

y(1) = 2050(12)^(1) = 24600

y(1) > y(0) -> growths