A company wants to have ​5 digit phone extensions with the first digit not being zero. How many different phone extensions are​ possible?

The logistic model for the population P is P = 75x = 400.

The number of deer population after 10 years is 1150.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

We have,

Deer:

Population capacity = 2500

Initial population = 400

Population after 4 years = 700

Now,

We can make two ordered pairs:

(0, 400) and (4, 700)

Now,

We can write an equation as,

P = mx + c

m = (700 - 400) / (4 - 0) = 300/4 = 75

And,

(0, 400) = (x, y)

400 = 75 x 0 + c

c = 400

So,

P = 75x + 400

This is the equation for the number of deers after x years.

Now,

The number of deers after 10 years.

x = 10

P = 75 x 10 + 400

P = 750 + 400

P = 1150

Thus,

The number of deer after 10 years is 1150.

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The final value of the investment is $689.10. Fill the table accordingly.

Compound interest is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods.

First year

Interest earned = 9/100 * $580 = $52.20

Second year

Balance + Interest = $580 + $52.20

Total balance = $632.20   (Note: Total balance = Balance + Interest )

Interest earned = 9/100 *  $632.20 = $56.90

Third year

Balance + Interest = $632.20 + $56.90

Total balance = $689.10

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Answer: $5.91

Step-by-step explanation:

Total borrowed = $29.96

Amount earned on Saturday

6 hours x $2.60 = $15.60

Amount earned on Monday

1 3/4 is the same as 1.75

1.75 hours X $2.60 = $4.55

Amount earned on Tuesday

1 1/2 is the same as 1.50

1.50 hours x $2.60 = $3.90

Total amount earned from Saturday, Monday, and Tuesday

$15.60 + $4.55 + $3.90 = $24.05

Amount Sarah owes her uncle

$29.96 borrowed

$24.05 earned

$29.96 - $24.05 = $5.91

Sarah owes $5.91.

Answer: A polynomial is an algebraic expression with 1, 2 or 3 variables, whereas, a multinomial is a type of polynomial with 4 or more variables.

Step-by-step explanation:

Answer:

Step-by-step explanation:

To calculate the simple interest earned on an investment of $9710 at a semiannual rate of 3.6% for 4 years, we need to use the formula:

I = Prt

where I is the interest, P is the principal (initial investment), r is the interest rate (as a decimal), and t is the time (in years).

In this case, the principal is $9710, the interest rate is 3.6% per year, or 0.036/2 = 0.018 per 6-month period (since the interest is compounded semiannually), and the time is 4 years, or 8 periods of 6 months each.

Plugging in these values, we get:

I = $9710 x 0.018 x 8 = $1392.24

Therefore, the simple interest earned on the investment is $1392.24. Rounding to the nearest cent, the answer is $1392.24.

Alexander's white paint will be more lighter.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is that in art class students are mixing black and white paint to make gray paint. Allison mixes 1 cup of black paint and 2 cups of white paint. Alexander mixes 6 cups of black paint and 11 cups of white paint.

We will compare the percent of white paint in a mixture.

We can write -

Therefore, Alexander's white paint will be more lighter.

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From the two plans for a set price the second graph in this issue is the right one.

The following is the definition of a linear function's slope and intercept:

y = mx + b.

where:

The rate of change is represented by the slope m.

The starting quantity is represented by the intercept b.

We have it for the plan with the fixed price:

Compared to the other plan, the slope is higher.

There is no intercept.

As a result, it is less expensive for fewer trips.

We have the following for the plan with the set price plus the fee:

Compared to the other plan, the slope is smaller.

There is an intercept that exceeds zero.

As a result, paying for more visits results in lower expenditures.

Hence, the second graph in this issue is the right one.

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Answer:

There are many expressions equivalent to this.

Step-by-step explanation:

Let's solve the equation.

In the parentheses, you cannot do ×+, so I will assume that × is meant to be a variable, x.

You can use distributive property to solve this.

3(2x + 5)

3 × 2x + 6x

3 × 5 = 15

6x + 15 cannot be done.

So, the answer to the equation is 6x + 15.

An Equivalent Expression

An equivalent expression can be 2(3x + 7.5)

Let's solve it.

2 × 3x = 6x

2 + 7.5 = 15

So, the answer to this equation is 6x + 15.

6x + 15 = 6x + 15.

2(3x + 7.5) = 3(2x + 5)

Answer:

The cost is 250

Step-by-step explanation:

Let's call the cost of the bench "x". The cost of the garden table is then 3x. The combined cost of the two items is $1000, so we can set up the following equation:

x + 3x = 1000

Combining like terms, we have:

4x = 1000

Dividing both sides by 4, we find:

x = 250

So the cost of the bench is $250.

The area of shaded region would be 15.7 in² which is a difference between the area of the circle and area of the triangle.

The entire space filled by a triangle's three sides in a two-dimensional plane is defined as its area. The fundamental formula for calculating the area of a triangle is A = 1/2 b h.

We know that;

The area of an equilateral triangle = (√3/4) a²

Here, a = 3

Hence, The area of the given triangle = (√3/4) × 3²

The area of the given triangle = 0.43 × 9 = 3.9 in²

And, The area of the circle = π (d/2)²

Here d = 5

The area of the circle = π (5/2)² = 19.63 in²

Thus, The area of shaded region = area of the circle - area of the triangle

The area of shaded region = 19.63 - 3.9 = 15.7 in²

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The complete question is shown in figure.

Answer:

(3x + 2y) (3x - 2y)

Step-by-step explanation:

a² - b² = (a + b) (a - b)

where a = 3x and b = 2y

Answer:

33 miles per hour

Step-by-step explanation:

To find the speed of the car in miles per hour, we need to divide the number of miles traveled by the time in hours. We can convert minutes to hours by dividing by 60. So, the time in hours is 45 minutes / 60 minutes/hour = 0.75 hours. Then, we can divide the distance traveled by the time to find the speed:

25 miles / 0.75 hours = 33.33 miles per hour

Rounding to the nearest whole number, the speed of the car was 33 miles per hour.

The rule for the arithmetic sequence in this problem is defined as follows:

[tex]a_n = 4.5 - 0.625(n - 1)[/tex]

An arithmetic sequence is a sequence of values in which the difference between consecutive terms is constant and is called common difference d.

The general rule of an arithmetic sequence is given as follows:

[tex]a_n = a_1 + (n - 1)d[/tex]

The common ratio for the sequence is given as follows:

d = 3.25 - 3.875 = 3.875 - 4.5 = -0.625.

The first term of the sequence is given as follows:

[tex]a_1 = 4.5[/tex]

Hence the rule is defined as follows:

[tex]a_n = 4.5 - 0.625(n - 1)[/tex]

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Using the distance formula, we can find the lengths of the sides of the triangle:

Side 1: From (1, −8) to (−3, 0)

d = √[(−3 − 1)² + (0 − (−8))²]

d = √[16 + 64]

d = √80

Side 2: From (−3, 0) to (−2, −7)

d = √[(−2 − (−3))² + ((−7) − 0)²]

d = √[1 + 49]

d = √50

Side 3: From (−2, −7) to (1, −8)

d = √[(1 − (−2))² + ((−8) − (−7))²]

d = √[9 + 1]

d = √10

To find the perimeter, we add the lengths of the three sides:

Perimeter = √80 + √50 + √10

Therefore, the exact perimeter of the triangle is:

Perimeter = √80 + √50 + √10

Drone 1 is traveling faster than Drone 2.

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

Given that;

The table and equation below show the proportional relationship between time, in seconds, x, and distance traveled, in feet, y, for two drones.

For drone 1;

The equation is,

⇒ y = 6x

For drone 2;

x = 8, 10, 13

y = 24, 30, 39

Now, For drone 1;

The distance in 8 seconds is,

⇒ y = 6x

⇒ y = 6 × 8

⇒ y = 48

The distance in 10 seconds is,

⇒ y = 6x

⇒ y = 6 × 10

⇒ y = 60

Thus, Drone 1 is traveling faster than Drone 2.

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The endpoints of an edge are its end-vertices. When two vertices are endpoints of the same edge, they are said to be neighbouring.

The limit of the normalised even iterations of a linear transformation can be used to obtain the similarity matrix. The square matrix in the particular case when G A=G B=G contains the similarity score between the vertices I and j of G as its I j)-th element.

The combination of two rays with the same terminal is called an angle. The vertex of the angle is the common terminal of the rays, which are referred to as the sides of the angle.

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Answer: -37j-2/24

Step-by-step explanation:

Step-by-step explanation:

a probability is always the ratio

desired cases / totally possible cases

when pulling one card out of 52 cards, the totally possible cases for the result are 52.

now, all we need to do is "counting" or calculating the desired cases for each problem.

a 3 or a heart is pulled.

it is important to really read this carefully : 3 OR a heart. not 3 and a heart (that would ask for the probability to pull the 3 of hearts card, as no other card would satisfy the criteria).

we have 13 cards of heart.

and we have 4 cards of the value 3. but one of them is already included in the 13 cards of heart.

so, we need to add only 3 to these 13 and get 16 desired cards.

the probability is therefore

16/52 = 4/13 = 0.307692308... ≈ 0.308

a face card OR a club is pulled.

face cards are Jack, Queen and King (the ones with faces on the cards). so, 3 per suit, 4 suits = 12 cards.

we have 13 cards of club.

3 of these cards are already in the group of face cards, so we need to add only 10 to to this group for the desired cases. and the probability is

22/52 = 11/26 = 0.423076923... ≈ 0.423

a face card AND a heart is pulled.

we have 13 cards of heart.

and now it is AND to be a face card (not OR like in the previous question).

there are only 3 face cards of heart. the probability is

3/52 = 0.057692308... ≈ 0.058

Answer:

A, There were about 204 principals in attendance

Step-by-step explanation:

In one exhibit room, there are 14 principals out of 60 people so the ratio is 14 to 60

If the ratio stays the same then, x is the number of principals in attendance at the conference, then

x/875 = 14/60

60x = 14(875)

60x = 12250

x = 12250/60 = 204

hope this helps.

Step-by-step explanation:

The probability of pulling out each type of coin at random can be found by dividing the number of coins of that type by the total number of coins in the bag. Let's assume the bag contains n quarters, m dimes, k nickels, and p pennies. The total number of coins in the bag would be n + m + k + p.

The probability of pulling out a quarter would be:

P(quarter) = n / (n + m + k + p)

The probability of pulling out a dime would be:

P(dime) = m / (n + m + k + p)

The probability of pulling out a nickel would be:

P(nickel) = k / (n + m + k + p)

And the probability of pulling out a penny would be:

P(penny) = p / (n + m + k + p)

It's important to note that the sum of the probabilities of all the possible outcomes must equal 1:

P(quarter) + P(dime) + P(nickel) + P(penny) = 1

Graph A and graph D represents quadratic function and linear function respectively.

Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points do not matter.

In the given figure,

In option A graph parabola represents the quadratic function.

In option B graph doe's not represents the function.

In option C graph doe's not represents the function.

In option D graph straight line represents the linear function.

Therefore, option A and option D are the correct answers.

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Answer:

Step-by-step explanation:

I am not sure what you mean with that question but a short definition of bullying is:

Bullying can result in physical injury, social and emotional distress, self-harm, and even death. It also increases the risk for depression, anxiety, sleep difficulties, lower academic achievement, and dropping out of school.

Answer:

880 feet; 0.166666666 miles or ⅙ of a mile

Step-by-step explanation:

First convert miles to feet so 1 mile is 5280 feet.

Now divide it by 2 because we're working with half a mile per 3 minutes.

Now we know that Kelly can run 2640 feet every 3 minutes. Divide that by three to get her pace for every minute and we know that she runs 880feet per minute. In miles that would be 0.166 or ⅙ of a mile

Step-by-step explanation:

the ratio is

1/2 mile per 3 minutes

= 1/2 / 3

now, we need to keep the value of that ratio unchanged but still transform the ratio (= a fraction) so that we get as ultimate denominator 1 instead of 3 (how far did he run in 1 minute).

what do we need to do to transform 3 to 1 ?

we need to divide by 3.

and because we have to keep the ratio value, we have to devide also the numerator by 3 :

1/2 / 3 × 1/3 / 1/3 = (1/2 × 1/3) / (3 × 1/3) = 1/6 / 1

so, we can read from the result directly :

when running with the same pace (ratio) for 1 minute, he will run 1/6 mile.

The cardinal number of G = 0 for the given set G = {x|x ∈ N and x is a negative}.

A set is defined as a group of objects in mathematics. Set names and symbols begin with a capital letter. According to set theory, a set's constituent parts can be included in anything.

The set is given in the question, as follows:

G = {x|x ∈ N and x is a negative}

We have to determine the cardinal number of set G = {x|x ∈ N and x is a negative}

Cardinal numbers, also known as Cardinals of a Set, are the numbers used to count the number of elements in a Set.

Simply expressed, the cardinal number of a set equals the number of items in a set.

Let A = {a, b, c, d}  be a set then Cardinal number of A is 4

Given G = {x|x ∈ N and x is a negative}

Here, x belongs to N, and a negative number

Since Natural Number (N) = 1, 2, 3, 4 ...

There is no negative value that corresponds to N.

Thus, G = { } or G is an empty set.

Hence, the cardinal number of G = 0

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The question seems incomplete, the complete question would be as:

Find the cardinal number of set G = {x|x ∈ N and x is a negative}

With help of integration, The volume of the  solid that results when the region bounded by y=√x , y=0, and x=16 is revolved about the line x=16 will be 42.66 cubic unit.

What exactly is integration?

The process of computing an integral is known as integration. Mathematicians utilise integrals to compute a variety of useful quantities such as areas, volumes, displacement, and so on. When we talk about integrals, we usually imply definite integrals. Antiderivatives are represented by indefinite integrals. Integration, along with differentiation, is one of the two major calculus concepts in mathematics (which measure the rate of change of any function with respect to its variables).

Integral Fundamental

A definite integral is one that has both upper and lower bounds. For X to lie, only a true line may be utilised. The Definite Integral is also known as a Riemann Integral.

From a to b, use ∫f(x)dx

indefinite integral

Integrals are defined without upper and lower limits. It looks like this:

A indefinite Integral is written as:

∫f(x)dx = F(x) + C

Where C might be any constant and the function f(x) is referred to as the integrand.

Now,

for volume of the   solid that results when the region bounded by y=√x , y=0, and x=16 is revolved about the line x=16.

volume= ∫√x dx for x=0 to 16

=x*√x/3/2

=64*2/3

=128/3

=42.66 cubic unit

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Answer: When the domain of the non-invertible function f(x)=(x+5)^2−8 is [−5,∞), the inverse of the function is not defined, and the domain of the inverse function is empty.

Step-by-step explanation:

The expression for (h·g)(x) is 4x²+17.8x+19.8.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

The given functions are g(x)=9+4x and h(x)=x+ [tex]2\frac{1}{5}[/tex].

Now, (h·g)(x)=h(x)×g(x)

= (x+ [tex]2\frac{1}{5}[/tex])×(9+4x)

= (x+11/5)×(9+4x)

= 9x+99/5+4x²+44x/5

= 9x+19.8+4x²+8.8x

= 4x²+17.8x+19.8

Therefore, the expression for (h·g)(x) is 4x²+17.8x+19.8.

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Answer:

Step-by-step explanation:

Given that bags of peanuts cost $0.93 each, booth rental costs $220 for the week, and your selling price is $2.90 per bag, you want expressions for cost, revenue, and profit, and you want these values when sales are 320 bags of peanuts for the week.

The total cost is the sum of fixed and variable costs. The fixed cost is the cost of booth rental, $220. The variable cost is the per-bag cost of peanuts, multiplied by the number of bags.

  total cost = 0.93n +220

The revenue is the selling price, multiplied by the number of bags sold:

  revenue = 2.90n

Profit is the difference between revenue and cost.

  profit = revenue -cost

  profit = (2.90n) -(0.93n +220)

  profit = 1.97n -220

  cost = 0.93·320 +220 = 297.60 +220 = $517.60 . . . total costs

  revenue = 2.90·320 = $928.00 . . . revenue

  profit = 1.97·320 -220 = 630.40 -220 = $410.40 . . . profit

__

Additional comment

The attached graph shows the cost (red), revenue (green), and profit (blue) curves. The vertical line identifies the values of these for 320 units sold.

It takes sales of 112 bags to pay the costs (break even).

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The surface area of the entire figure is 1764 ft².

A rectangular prism is a three-dimensional shape that has six faces, where each face is a rectangle. It is also sometimes referred to as a rectangular cuboid.

A rectangular prism has eight vertices (corners), 12 edges, and six faces. The opposite faces of a rectangular prism are parallel and congruent, and the angles formed between adjacent faces are all right angles (90 degrees).

The volume of a rectangular prism can be calculated by multiplying the length, width, and height of the prism. The formula for the volume of a rectangular prism is given by V = l x w x h, where V is the volume, l is the length, w is the width, and h is the height of the prism.

We can begin by finding the dimensions of the rectangular prism and the cuboid. Since the side of the rectangular prism is 9 ft, it must be the height of the entire figure. We can find the dimensions of the cuboid by subtracting the height of the rectangular prism from the height of the entire figure:

height of cuboid = 19.8 ft - 9 ft = 10.8 ft

width of cuboid = 15 ft

length of cuboid = 12 ft

Now we can find the surface area of the entire figure by adding the surface areas of the rectangular prism and the cuboid. The surface area of a rectangular prism is given by:

2lw + 2lh + 2wh

where l, w, and h are the length, width, and height of the prism, respectively. Substituting in the values we have:

surface area of rectangular prism = 2(9)(9) + 2(9)(19.8 - 9) + 2(9)(15) = 486 + 162 + 270 = 918 ft²

The surface area of a cuboid is given by:

2lw + 2lh + 2wh

where l, w, and h are the length, width, and height of the cuboid, respectively. Substituting in the values we have:

surface area of cuboid = 2(15)(9) + 2(12)(9) + 2(15)(12) = 270 + 216 + 360 = 846 ft²

Therefore, the surface area of the entire figure is:

surface area = surface area of rectangular prism + surface area of cuboid = 918 + 846 = 1764 ft²

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Answer:

C(t) = 0.50 * t + 2.50

Step-by-step explanation:

The function C(t) to represent the cost of a taxicab ride can be written as:

C(t) = 2.50 + 0.50 * t

where t is the distance traveled in tenths of a mile.

The slope of the graph of this function is 0.50, which represents the cost per tenth of a mile.

The y-intercept of the graph of this function is 2.50, which represents the fixed fee that must be paid regardless of the distance traveled.

So, the equation of the graph of this function is:

C(t) = 0.50 * t + 2.50