A student was trying to write an exponential function to represent a fish population in a local stream decreasing at a rate of​ 3% per year. The original population was​ 48,000. The student made an error when writing their exponential function. Find and explain the error in the​ student’s work below.
y=48,000(1.03)^x

If Pete sells 50 pizzas, he will make a profit of $75. The equation can be used to determine the profit is y = 5.50x - 200.

Pete's Pizzas charges $5.50 per pizza and has spent $200 in supplies to start his business.

We can use the following equation to determine the total profit he will make after he sells x amount of pizzas:

y = 5.50x - 200

where y is the total profit, 5.50 is the revenue per pizza, x is the number of pizzas sold, and -200 is the fixed cost for the supplies.

For example, if Pete sells 50 pizzas, we can plug in the values into the equation:

y = 5.50 * 50 - 200

y = 275 - 200

y = 75

So, if Pete sells 50 pizzas, he will make a profit of $75. The equation can be used to determine the profit for any number of pizzas sold by simply changing the value of x.

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Yes, you can relate a given quantity to the indicated amount using more than one symbol.

In mathematics, symbols are used to represent mathematical objects and operations, making it easier to understand and communicate mathematical ideas.

Each symbol has a specific meaning and can be used in different ways to represent the same quantity.

For example, the number 7 can be represented by the numeral 7, the Roman numeral VII, or even the symbol 7 in scientific notation. All of these symbols represent the same quantity, but they each have a different context and use.

The numeral 7 is commonly used in everyday life, the Roman numeral VII is used in ancient times and in some specific contexts, and the scientific notation 7 x 10⁰ is used in scientific and mathematical calculations.

Similarly, in algebra, a variable such as x can represent a quantity and can be used in different ways to represent the same value.

For example, the equation x + 3 = 6 can be solved for x to find that x = 3. This same value can also be represented by the expression 3x, which shows that x is equal to 3.

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Answer:

60 people

Step-by-step explanation:

Before

C:A

2:3

After

C:A

3:2

We know that the number of adults never change.

Before

C:A

4:6

After

C:A

9:6

difference in units of children= 9-4

= 5

5 units= 30

1 unit= 30÷5

= 6

total units [before]= 4+6

= 10

10 units= 6×10

=60

The ordered pairs that are solutions to y + 2 = -3(x - 4) include :

To find the ordered pairs, insert the x value in an ordered pair, into the equation. If the y value that you are given is the same as the one in the ordered pair, then the ordered pair is a solution to the equation.

Ordered pair ( 5, - 5 ) :

y + 2 = - 3 ( 5 - 4 )

y + 2 = - 3

y = - 3 - 2

y = - 5

Ordered Pair ( 2, 4 )

y + 2 = - 3 ( 2 - 4 )

y + 2 = 6

y = 6 - 2

y = 4

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Options for this question are:

Arun walked 5 km to east and then 12km to north. By joining the starting point and the end point by straight line we will get a right angled triangle, hypotenuse of which will tell how far is he from his starting point.

The square on the hypotenuse's area is equal to the sum of the two squares on the legs (a and b) (c). Pythagoras, a Greek philosopher who was born in 570 BC, is honored by having his theorem named after him. The theorem has already been shown more than once through various techniques, possibly greater than any other mathematical theorem. The hypotenuse side of a right-angled triangle's square is equal to the total of its other two sides, according to Pythagoras' Theorem. These right triangle three sides are known as the Perpendicular, Base, and Hypotenuse.

So Pythagoras theorem,

H²= 5² + 12²

H²= 25 + 144

H² = 169

H = 13

So, he will be 13 km far away from his starting point.

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Answer:

Below

Step-by-step explanation:

If the men are indistinguishable   and the women are too, then

6 w  5 m    

7 w 4 m

8 w   3 m

      3 ways

IF they ARE distinguishable it becomes a much larger, complex calculation:

8 C 6 * 10 C 5   +  8 C 7 * 10 C 4   +  8 * 10 C 3  

  ( is THIS what you are studying ? )

Answer:

-1/16

Step-by-step explanation:

5/16 - 3/8 =

To subtract fractions, you need a common denominator. The least common denominator (LCD) of 16 and 8 is 8.

= 5/16 - 6/16

= -1/16

Answer:x=\frac{b-1}{a-d}

Step-by-step explanation:

The system of linear equations shown in the graph has no solution.

Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.

Both linear equations with one variable and those with two variables exist.

Given the coordinates of two lines,

line 1: line passes from (0, 3) and (3, 2)

and slope of the line is given by,

m = (y₂ - y₁)/(x₂ - x₁)

m = (2 - 3)/(3 - 0)

m = -1/3

Line 2: line passes from (0, -2) and (3, -3)

slope =  (y₂ - y₁)/(x₂ - x₁)

m = (-3 - (-2))/(3 - 0)

m = -1/3

since both, the lines have the same slope so both lines will be parallel,

If two lines are parallel, they will never intersect and so there is no solution to the given system of equations.

Hence lines will have no solution.

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The correct answer is option c. There are no real-valued functions that have a domain of all real numbers and a range of all integers.

A function maps an input (or domain) to a unique output (or range). In order for a function to have a domain of all real numbers, it must take any real number as an input and provide a unique output. However, for a function to have a range of all integers, it must be the case that every output is an integer.

Since the real numbers are not countable and the integers are countable, there can be no function that maps every real number to a unique integer. In other words, there is no one-to-one correspondence between the real numbers and the integers, which means that it is not possible to find a function that maps every real number to an integer.

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Complete Question:

which function(s) has the following properties? there may be more than one answer, so select all that apply.

Answer:

2 - √5 is an irrational number

Step-by-step explanation:

The sum or difference between a rational number and an irrational number is always irrational.

Here 2 is a rational number and √5 is an irrational number. Hence 2 - √5 is an irrational number.

Answer:

D

Step-by-step explanation:

15+3x=15

15-15+3x=15-15

3x=0

3x/3=0/3

x=0

Answer:Not to simplify

Step-by-step explanation:

Answer:

No

Step-by-step explanation:

9/10 is already in its simplest form. It cannot be further simplified as it is a fraction with two prime numbers in its numerator and denominator.

A limit describes a function's value as it gets closer to a certain value as its inputs increase. All calculus is based on the concept of a limit.

There are one-sided limits (left- and right-hand limits), infinite limits, and limitations at infinity in addition to regular, two-sided limits.

Let's look at an example to better grasp what limits are. Beginning with the function f (x) = x + 2 f(x) = x + 2 f(x) = x + 2f, left parenthesis, x, right parenthesis, equals, x, plus, 2. The value f approaches as we move closer and closer to x = 3 x=3 x=3, which is the limit of f at x = 3 x=3 x=3.

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The values of the two limits are lim x->33- g(x) = -15 and lim x->33+ g(x) = -6.

Option (B) is correct.

What is a limit in calculus?

The limits in mathematics describe the behavior of a function as the input approaches a certain value. The symbols for limits are "lim" followed by the variable and the value that the variable is approaching, with an arrow indicating the direction of the approach.

For the given function g(x), we have the following limits:

lim x->33- g(x) = -15.1

This means that as x approaches 33 from below, the value of g(x) approaches -15.1. We can see this from the values in the table, as x gets closer to 33 from below, g(x) gets closer to -15.1.

lim x->33+ g(x) = -6.1

This means that as x approaches 33 from above, the value of g(x) approaches -6.1. We can see this from the values in the table, as x gets closer to 33 from above, g(x) gets closer to -6.1.

So, the values of the two limits are lim x->33- g(x) = -15.1 and lim x->33+ g(x) = -6.1.

Hence, The values of the two limits are lim x->33- g(x) = -15 and lim x->33+ g(x) = -6.

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Answer:

24 bog ole hotdogs

Step-by-step explanation:

Answer:

12 hot dogs in 30 minutes

Step-by-step explanation:

1. Write it as a fraction

      1. 2/5

2. Write what we know of the answer as a fraction

     1. ?/30

3. For the denominator to get to 30, we must multiply 5 by 6. However, we also have to multiply the numerator by 6.

        1. 2*6=12.

4. Therefore, the answer is 12/30, or he will eat 12 hot dogs in half an hour.

Applying the secant-secant theorem, the value of x is: 12.

The secant-secant theorem states that if you draw two lines from a point outside a circle that intersect the circle at two different points, then the product of the length of one line segment and the length of the portion of the line outside the circle is equal to the product of the length of the other line segment and the length of its portion outside the circle.

Based on the secant-secant theorem, we have:

EF * ES = ED * EC

Substitute the values:

8(8 + 10) = 9(2x - 17 + 9)

Solve for x:

144 = 18x - 72

144 + 72 = 18x

216 = 18x

216/18 = x

x = 12

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Note that where in a Rhombus ACDB, m∠CDB = 60 degrees and BC = 10. The diagonals cross at point M. The length of the side of ACDB is 10.

A rhombus is a quadrilateral with four equal-length sides in planar Euclidean geometry. The term equilateral quadrilateral refers to the fact that all of its sides are the same length.

Note that the above-described Rhombus is described accordingly. Since the diagonals are perpendicular to each other and bisect one another each at an inner angle that is 90° each, then we can say that;

∠MDC = 30°
MC = 1/2BC

= 1/2 * 10
= 5

Thus,

DC = MC/Sin30°
= 5/1/2
= 5 * 2
= 10

Thus, the measure of a side of a Rhombus - ACDB is 10.

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The correct explanation is Chen read for less time as compared to Sierra, as 420 minutes is less than 220 minutes.

Time is an important aspect of reading as it determines how much one can read in a certain period.

In this case, we have two individuals, Sierra and Chen, who read for different times in a week. To determine which one read more time, we need to convert the units of time into minutes, the same unit of measurement.

D. Chen read for less time because an hour a day for 7 days is equal to 210 minutes.

This explanation is correct as 1 hour a day for 7 days is equal to 420 minutes, not 210 minutes.

Therefore, the correct explanation is option (D).

Complete Question:

Sierra read for 220 minutes in 1week. Chen read for an hour a day for 7 days. Which explanation is correct?

A. Sierra read for more time because 220 is greater than

B. Sierra read for less time because minutes are less than hours.

C. They read for the same amount of time because 1 week is equal to 7 days.

D. Chen read for less time because an hour a day for 7 days is equal to 210 minutes.

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Figure ABCD has vertices A(-3, 2), B(2, 2), C(2, -4), and D(-3, -2) then the area of Figure ABCD be 25 square units.

A vertex in geometry is a location where two or more curves, lines, or edges come together. The intersection of two lines to form an angle, as well as the corners of polygons and polyhedra, are vertices according to this definition.

A polygon's vertex is a location where the sides or edges of the item or two rays or line segments meet. Vertex is a noun, whereas vertices is the plural. Vertices are the points at which the edges of the three-dimensional shape converge. Edges are the lines that separate two faces, while faces are flat surfaces.

The area of the trapezoid exists equal to

A = 1/2 (AD + BC) AB

To estimate the distance between the points in the graph we have

AD = 4 units, BC = 6 units and AB = 5 units

substitute the values in the above equation, we get

A = 1/2 (4 + 6)5 = 25 square units

Therefore, the correct answer is option c) 25 square units.

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It is important to note that the probability of an exact match at all 16 loci is very low, as even small differences in the number of repeats at each locus can result in different genotypes. This makes it unlikely to find two individuals with an exact match at all loci.

The field of mathematics concerned with probability is known as probability theory. Although there are various distinct interpretations of probability, probability theory approaches the idea rigorously mathematically by articulating it through a set of axioms. The probability is a measure of the possibility that an event will occur. It assesses the event's certainty. P(E) = Number of Favourable Outcomes/Number of Total Outcomes is the probability formula.

Here,

To calculate the probability of an identical match at all 16 STR loci, you would need to determine the frequency of each unique genotype at each locus, and then multiply the frequencies of each unique genotype to obtain the probability of all 16 loci having the same genotype in two individuals.

This probability would be based on the genetic makeup of the population of elephants that the individuals are drawn from, and the specific alleles present at each locus in each individual.

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Following Answers are:

Percentage is a way to express a number as a fraction of 100. It is often used to represent ratios and proportions in a more convenient and understandable form, especially in financial and statistical contexts. For example, 50% means 50 per 100, or half of a given quantity. It is denoted using the symbol "%".

To calculate the 10% down payment required by the bank, you can use the following formula:

Down payment = 2700 x 10%

                          = $270

To calculate the loan amount, you can subtract the down payment from the total cost of the moped:

Loan amount = 2700 - 270

                      = $2430

To calculate the monthly loan payment, you need to know the interest rate, the loan amount, and the number of months in the loan term. You can use the following formula to calculate the monthly payment:

Monthly payment = (Loan amount x Interest rate) / (1 - (1 + Interest rate)^(-Number of months in loan term))

In this case:

Monthly payment = ($2430 x 8%) / (1 - (1 + 8%)⁻⁶)

Monthly payment = $44.38

The breakdown of each of the 6 payments would be $44.38 per month.

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The All are equivalent expression except 2/4 - 1/2 given in the question.

A mathematical expression known as an algebraic expression is one that includes variables, coefficients, constants, and operations like addition, subtraction, multiplication, and division. Generally speaking, two of something are regarded as being equivalent. Similar to this, equivalent mathematical expressions are those that are true even when they appear to be different. When the values are put into the formula, however, both expressions yield the same result.

Expression Equivalent

X - 2/4 Equivalent to 1/2 X - 1

2/4 - X Equivalent to X - 1/2

2/4 - 1/2 Not Equivalent to 1/2 X - 1 or X - 1/2

X + 1/2 Equivalent to X - 1/2

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Answer:

Jamie has $12.50 of her allowance left if the books cost $2.50 each.

Step-by-step explanation:

To calculate this, first calculate the total cost of the books:

5 books x $2.50/book = $12.50.

Then subtract the cost of the books from the amount Jamie has saved:

$38 - $12.50 = $25.50.

Finally, subtract the cost of the books from the amount Jamie has saved to get the amount she has left:

$25.50 - $12.50 = $12.50.

Answer:

$25.50

Step-by-step explanation:

We know Jamie bought 5 books, each worth $2.50, d. We need to know the cost of all five, so we’ll go ahead and multiply 5 times $2.50 to get $12.50.

Since we know how much the books cost, all we have to do now is subtract the amount she spent from her allowance. $38.00 - $12.50 is 25.50, the amount of money Jamie has left.

[tex]\frac{s}{-2 + 10} = 13[/tex]

To solve this, we first remove any fraction. So we have to multiply "-2 + 10" on each sides:

[tex]s = 13(-2+10)\\s = 13(8)\\s = 104[/tex]

If any step didn't make sense, tell me and I will help you :)

Answer:

f(1/7) = 3 3/4 in simplest form.

Step-by-step explanation:

To find the value of f(1/7), we can substitute 1/7 for x in the function:

f(1/7) = -7/4 * 1/7 + 4

f(1/7) = -7/4 * 1/7 + 4

f(1/7) = -7/28 + 4

f(1/7) = 4 - 7/28

f(1/7) = 4 - 1/4

f(1/7) = 3 3/4

So f(1/7) = 3 3/4 in simplest form.

Answer:

7 units

Step-by-step explanation:

The point is 4 units from the x axis and 3 units from the y axis.

4 + 3 = 7

Answer:

Nick can bake 16 cupcakes at most

Step-by-step explanation:

If you divide 200 by 16, you get 16.667. Because .667 is not a full cupcake, you cannot round up to get 17 cupcakes.

If you have any questions, feel free to ask in the comments. If you find my answer helpful, please consider marking brainliest. Hope this helps!

The steps to solve the equations are his below.

Here are the steps to solve a system of two linear equations:

Write the equations in slope-intercept form (y = mx + b) or standard form (ax + by = c).

Identify the coefficients and the constant terms of each equation.

Choose one equation and solve for one variable (e.g. x or y).

Substitute the value of the variable found in step 3 into the other equation.

Solve for the other variable by rearranging the equation obtained in step 4.

Substitute the values of both variables back into either equation to check the solution.

Graph the two equations on the same set of axes to visually check if the solution is correct.

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Domain of function is in Set Builder Notation is, {x | x ≥ 7 }.

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

The function is,

⇒ f (x) = √(x-7) / (x³ + 1)

Now, We can find the domain of function as;

⇒ f (x) ≥ 0

⇒ √(x-7) / x³ + 1 ≥ 0

⇒ √ (x - 7) ≥ 0

⇒ x - 7 ≥ 0

⇒ x ≥ 7

Thus, Domain of function is in Set Builder Notation is, {x | x ≥ 7 }.

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