Please help me. I’ll mark you as brainliest if correct

Answer:

12,13 and 14

Step-by-step explanation:

Let the three consecutive integers be n, n+1 and n+2

ATQ,

The sum of twice the second integer and 4 times the third integer is two less than seven times the first integer.

[2(n+1)+4(n+2)] = 7n-2

or

2n+2+4n+8=7n-2

Taking like terms together,

6n-7n = -2-8-2

n = 12

So,

First integer = 12

Second integer = 12+1 = 13

Third integer = 12+2 = 14

Hence, three consecutive integers are 12,13 and 14.

It would take 21 weeks for the population to surpass 16,000.

The insect population P in a certain area fluctuates with the seasons and is estimated by the function P = 15,000 + 2500 sin(πt/52), where t is given in weeks.

For the population to surpass 16,000, we can set up the following equation:

15,000 + 2500 sin(πt/52) = 16,000

Subtracting 15,000 from both sides, we get:

2500 sin(πt/52) = 1000

Dividing both sides by 2500, we get:

sin(πt/52) = 0.4

We know that sin(πt/52) is positive when t is between 0 and 52 and between 104 and 156 since sine is positive in the first and second quadrants. Therefore, we can write:

πt/52 = sin⁻¹(0.4)

Multiplying both sides by 52/π, we get:

t = (52/π) sin⁻¹(0.4)

Using a calculator, we can evaluate sin⁻¹(0.4) to be approximately 0.4115 radians.

t = (52/π) (0.4115)

t = 21.02

Therefore, it would take 21 weeks for the population to surpass 16,000.

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Answer:

Mrs. Powers spent $3.96 on each student

Step-by-step explanation:

Divide the total amount of money she spent by 21 (students)

Answer: A

Step-by-step explanation:

Answer:

18 is less then 23

Step-by-step explanation:

The value of n is 8.

Binomial theorem is the method of expanding an expression consisting of two terms raised to any power.

Using the expansion of Binomial theorem, we can write,

(2 + 3x)ⁿ = ⁿC₀ (2)ⁿ (3x)⁰ + ⁿC₁ (2)ⁿ⁻¹ (3x)¹ + ⁿC₂ (2)ⁿ⁻² (3x)² + ⁿC₃ (2)ⁿ⁻³ (3x)³ + ⁿC₄ (2)ⁿ⁻⁴ (3x)⁴ + .............

Coefficient of x³ is  ⁿC₃ (2)ⁿ⁻³ (3)³ and the coefficient of x⁴ is ⁿC₄ (2)ⁿ⁻⁴ (3)⁴.

Ratio of these coefficients is 8 : 15.

[ⁿC₃ (2)ⁿ⁻³ (3)³] / [ⁿC₄ (2)ⁿ⁻⁴ (3)⁴] = 8 / 15

Simplifying,

(4 × 2) / [(n - 3) 3] = 8/15

8 / 3n - 9 = 8 /15

Equating, we have,

3n - 9 = 15

3n = 24

n = 8

Hence the value of n is 8.

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The profit made as a function of x ;

Let :

Number of units produced = x

Profit per unit = $3

Fixed cost = $17,000

Total profit made : Revenue - Cost of production

Profit, P(x) = (profit per unit × number of units) - Fixed cost

Profit, P(x) = 3x - 17,000

B.)

When x = 20,000

P(20000) = 3(20000) - 17,000

Profit = 60000 - 17,000

Profit = 43,000

When x = 5000

P(5000) = 3(5000) - 17,000

Profit = 15000 - 17,000

Profit = - 2000

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The total profit as a function of x is P(x) = 3x - 17,000

(A) The profit is $43,000

(B) The loss is $2,000

The given parameters;

The following equations will be set up as follows;

Total cost price = 17,000 + x(y)

Total selling price = x(y + 3)

The total profit as a function of x is calculated as;

total Profit = total selling price - total cost price

total Profit = x(y+3) - 17,000 - xy

total Profit = xy + 3x - 17,000 - xy

total Profit = 3x - 17,000

P(x) = 3x - 17,000

(A) The profit or loss when x = 20,000 units are produced;

P(20,000) = 3(20,000) - 17,000

P(20,000) = 60,000 - 17,000

P(20,000) = $43,000

The profit is $43,000

(B) The profit or loss when x = 5,000 units are produced;

P(5,000) = 3(5,000) - 17,000

P(5,000) = 15,000 - 17,000

P(5,000) = - $2,000

The loss is $2,000

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well, we're assuming all along that Merina owes Bradford $2000, because in the 1st scenario, she was going to pay twice $1000.

on the 2nd scenario, she'll be paying the same $2000 but split 7 months from now and then 7 months later, same 2000 bucks, at which point Bradford applied 8.5% interest.

using those assumptions, since the wording is not quite clear, we can say that Merina is simply paying 2000 bucks plus the 8.5%

\(\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{8.5\% of 2000}}{\left( \cfrac{8.5}{100} \right)2000}\implies 170 \\\\[-0.35em] ~\dotfill\\\\ \cfrac{\stackrel{principal}{2000}~~ + ~~\stackrel{interest}{170}}{2}\implies \stackrel{\textit{two equal payments of}}{1085}\)

The number of degrees below zero is given by A = 56° F

Regardless of the sign, a modulus function returns the magnitude of a number. The absolute value function is another name for it.

It always gives a non-negative value of any number or variable. Modulus function is denoted as y = |x| or f(x) = |x|, where f: R → (0,∞) and x ∈ R.

The value of the modulus function is always non-negative. If f(x) is a modulus function , then we have:

If x is positive, then f(x) = x

If x = 0, then f(x) = 0

If x < 0, then f(x) = -x

Given data ,

Let the initial temperature be represented as T

Let the number of degrees below zero be A

Now , the value of T is

T = -56° F

From the modulus function , we get

The value of the modulus function is always non-negative.

So , the measure of A = | T |

A = | -56 |

A = 56° F

Hence , the number of degrees below zero is 56° F

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Answer:

Step-by-step explanation:

No, there would have to be two point that have identical x coordinates

Answer: 120

Step-by-step explanation: I got it right, hope this helps ✨

Answer:

he has I20 different ways to put the books

Step-by-step explanation:

to solve this you would multiply 5x4x3x2 this is how many different combinations he can but the note book on the shelf. 5x4x3x2 is equal to 120

Answer:

3 and 16

Step-by-step explanation:

Answer:

it is A

Step-by-step explanation:

Answer:

I believe the answer is six-hundred thousand (600000). That's if I read your question right. I'm not sure what you were asking exactly.

Step-by-step explanation:

6 (10000 x 10)

6 (100000)

600000

Answer:

Answer: 6,240

Step-by-step explanation:

Answer:

you can make 12 cans of them

Answer: \(\dfrac{9}{66892280}\)

Step-by-step explanation:

Number of combinations of r things from n things = \(^nC_r=\dfrac{n!}{r!(n-r)!}\)

Number of combinations of choosing 9 cards out of 52 = \(^{52}C_9=\dfrac{52!}{9!(52-9)!}=3679075400\)

Total face cards = 12

Number of combinations of choosing 8 face cards = \(^{12}C_8=\dfrac{12!}{8!(12-8)!}=495\)

Required probability = \(\dfrac{495}{3679075400}=\dfrac{9}{66892280}\)

Hence, the probability that the hand contains exactly 8 face cards. = \(\dfrac{9}{66892280}\)

Answer:

the answer is 45.9

Step-by-step explanation:

Answer:

45.9

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

We can use the distance formula

11. d =sqrt( (y2-y1)^2 + (x2-x1) ^2)

  = sqrt( (-3 --5)^2+(-6 - -1)^2)

  = sqrt( (-3+5)^2 + (-6+1)^2)

  = sqrt( 2^2 + (-5)^2)

  = sqrt (4+25)

  = sqrt(29)

12. Using the points ( 1,3) and (4,-1)

d =sqrt( (y2-y1)^2 + (x2-x1) ^2)

  = sqrt( (-1-3)^2+(4-1)^2)

  = sqrt( (-4)^2+(3)^2)

 = sqrt(16+9)

 =sqrt(25)

 =5

Answer:

11. d =sqrt( (y2-y1)^2 + (x2-x1) ^2)

 = sqrt( (-3 --5)^2+(-6 - -1)^2)

 = sqrt( (-3+5)^2 + (-6+1)^2)

 = sqrt( 2^2 + (-5)^2)

 = sqrt (4+25)

 = sqrt(29)

12. Using the points ( 1,3) and (4,-1)

d =sqrt( (y2-y1)^2 + (x2-x1) ^2)

 = sqrt( (-1-3)^2+(4-1)^2)

 = sqrt( (-4)^2+(3)^2)

= sqrt(16+9)

=sqrt(25)

=5

Step-by-step explanation:

Answer:

41 meters

Step-by-step explanation:

\(\frac{31}{64}\) = \(\frac{19.8}{x}\)

31x = (19.8)(64)

31x = 1267.2  Divide both sides by 31 and round

x = 41

Using the figure the missing sides are

A rectangle is a type of quadrilateral that has four right angles and two pairs of opposite sides that are parallel and equal in length. Some of the properties of a rectangle will b used to find the value of the missing sides as follows

∠ BCD = 90 degrees (All four angles are right angles (90 degrees)).

∠ ABD = 6 degrees (alternate angles are equal)

∠ CBE = 90 - 6  = 84 degrees

∠ ADE = ∠ CBE = 84 degrees (alternate angles are equal)

∠ AEB = ∠ DEC (vertical angles)

∠ DEC = 180 - 6 - 6= 168 degrees (Diagonals are equal, isosceles triangle)

∠ DEA = 180 - ∠ DEC (Linear pair theorem)

∠ DEA = 180 - 168 = 12 degrees

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The matching of items and their corresponding descriptions are 1. Domain, 2.Output, 3. Input, 4. Relation, 5. Function, and 6. Range.

1. Domain - the first element of a relation or function; also known as the input value.

3. Input - the x-value of a function.

6. Range - the second element of a relation or function; also known as the output value.

4. Relation - any set of ordered pairs (x, y) that are able to be graphed on a coordinate plane.

2. Output - a relation in which every input value has exactly one output value.

5. Function - the y-value of a function.

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Answer:

78.59$

Step-by-step explanation:

The class width used for the frequency distribution is 6.

The class midpoint for the class 23-29 is 26.

The class midpoint for the class 30-36 is 33.

The class midpoint for the class 37-43 is 40.

To find the class width of the frequency distribution, we need to determine the range of each age class. The range is the difference between the upper and lower boundaries of each class. Looking at the table, we can see that the class boundaries are as follows:

23-29

30-36

37-43

For the class 23-29, the lower boundary is 23 and the upper boundary is 29. To find the class width, we subtract the lower boundary from the upper boundary:

Class width = 29 - 23 = 6

So, the class width for the frequency distribution is 6.

To find the class midpoint for each class, we take the average of the lower and upper boundaries of each class.

For the class 23-29:

Class midpoint = (23 + 29) / 2 = 52 / 2 = 26

For the class 30-36:

Class midpoint = (30 + 36) / 2 = 66 / 2 = 33

For the class 37-43:

Class midpoint = (37 + 43) / 2 = 80 / 2 = 40

So, the class midpoint for the class 23-29 is 26, for the class 30-36 is 33, and for the class 37-43 is 40.

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Answer:

The answer is [   ]

Step-by-step explanation:

Since both 40 males and 50 females, we add them to get 90 ppl in all. 50 of those 90 are female. Find that ration, 50:90, as a percentage. That would be 55.5% (i think)

Answer:

55.55555%

Step-by-step explanation:

50/90

Answer:

Step-by-step explanation:

3) 15,39,65

_________

5 )5,13,65

--------------

13  )1,13,13

----------------

   |  1,1,1

L.C.M.=3×5×13=195

They will chime together after 195 minutes.

The quadratic function f(x) =\(3(x+3)^2 - 7\) has a minimum at x = -1, and the minimum value is 5.

To determine whether the quadratic function f(x) =\(3(x+3)^2 - 7\)has a minimum or maximum, we can examine the coefficient of the x^2 term, which is positive (3 in this case).

When the coefficient of the x^2 term is positive, the parabola opens upward, indicating that the function has a minimum value. The vertex of the parabola represents the minimum point.

Now let's find the coordinates of the vertex, which will give us the minimum value of the function.

The general form of a quadratic function is f(x) =\(ax^2 + bx + c\), where the vertex can be found using the formula:

x = -b / (2a)

In our case, a = 3 and b = 3*2 = 6 (from (x+3)^2).

Substituting the values into the formula, we have:

x = -6 / (2 * 3)

x = -6 / 6

x = -1

To find the y-coordinate of the vertex, we substitute the x-value (-1) into the function:

\(f(-1) = 3((-1)+3)^2 - 7\)

\(f(-1) = 3(2)^2 - 7\)

f(-1) = 3(4) - 7

f(-1) = 12 - 7

f(-1) = 5

The graph of this function will have a downward-opening parabola, and the vertex will be the lowest point on the curve.

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The correct answer is (a). P′(2005) represents the growth rate (in people per year) of the population in 2005.

This is because P′(t) is the derivative of P(t), which measures the rate of change of P(t) concerning t.

In other words, P′(t) tells us how fast the population is changing at a given year t.

The units of P′(t) are the same as the units of P(t) divided by the units of t, which are millions of people per year.

Therefore, P′(2005) gives the number of millions of people by which the population changed in 2005. To find the actual number of people, we would have to multiply P′(2005) by one million.

The derivative can help us analyze the behavior of the population function, such as it's increasing or decreasing intervals, its maximum or minimum values, and its concavity or inflection points. The derivative can also help us model and predict the future trends of the population based on the current data and assumptions.

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Answer:

660.4 mm

Step-by-step explanation:

Since 1 inch is equal to 25.4 millimeters, we can multiply 25.4 by 26 to see how many millimeters 26 inches is. You can also think of this as a proportion:

26:x = 1:25.4

26.4 times 26 is equivalent to 660.4, so we can conclude that 26 inches are equivalent to 660.4 millimeters.

If you have any further questions or need clarification on anything, let me know!