An ant colony is built by 200 ants. The number of ants triples each week. How many ants will be in the colony at the end of the eighth week?

Answer:

1/4+1/3+1/8

=17/24

Step-by-step explanation:

1-17/24

=7/24

7/24×240

=70

Answer:

66 es pero que te ayude ■■♤♤

The x-intercepts of the graph of f(x) are x = 3/2 and x = 1,the Vertex of the graph of f(x) is (5/4, 3/8), and it is a minimum point, The vertex is at (5/4, 3/8). This is the minimum point of the graph.

Part A: To find the x-intercepts of the graph of f(x), we set f(x) equal to zero and solve for x.

2x^2 - 5x + 3 = 0

To factor this quadratic equation, we look for two numbers that multiply to give 3 (the coefficient of the constant term) and add up to -5 (the coefficient of the linear term). These numbers are -3 and -1.

2x^2 - 3x - 2x + 3 = 0

x(2x - 3) - 1(2x - 3) = 0

(2x - 3)(x - 1) = 0

Setting each factor equal to zero, we get:

2x - 3 = 0   -->   x = 3/2

x - 1 = 0   -->   x = 1

Therefore, the x-intercepts of the graph of f(x) are x = 3/2 and x = 1.

Part B: To determine whether the vertex of the graph of f(x) is a maximum or a minimum, we look at the coefficient of the x^2 term, which is positive (2 in this case). A positive coefficient indicates that the parabola opens upwards, so the vertex will be a minimum.

To find the coordinates of the vertex, we can use the formula x = -b/2a. In the equation f(x) = 2x^2 - 5x + 3, the coefficient of the x term is -5, and the coefficient of the x^2 term is 2.

x = -(-5) / (2*2) = 5/4

Substituting this value of x back into the equation, we can find the y-coordinate:

f(5/4) = 2(5/4)^2 - 5(5/4) + 3 = 25/8 - 25/4 + 3 = 3/8

Therefore, the vertex of the graph of f(x) is (5/4, 3/8), and it is a minimum point.

Part C: To graph f(x), we can use the information obtained in Part A and Part B.

- The x-intercepts are x = 3/2 and x = 1. These are the points where the graph intersects the x-axis.

- The vertex is at (5/4, 3/8). This is the minimum point of the graph.

We can plot these points on a coordinate plane and draw a smooth curve passing through the x-intercepts and the vertex. Since the coefficient of the x^2 term is positive, the parabola opens upwards, and the graph will be concave up.

Additionally, we can consider the symmetry of the graph. Since the coefficient of the linear term is -5, the line of symmetry is given by x = -(-5) / (2*2) = 5/4, which is the x-coordinate of the vertex. The graph will be symmetric with respect to this line.

By connecting the plotted points and sketching the curve smoothly, we can accurately graph the function f(x).

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Answer:

A

Step-by-step explanation:

(y-5) / (7-5) = (x-1) / (2-1)

(y-5) / 2 = x-1

y-5 = 2x -2

y = 2x +3

Based on the information given the new balance is $289.72.

First step is to calculate the finance charge

\(\text{Finance charge}=205.16\times(0.144\div12 \ \text{months})\)

\(\text{Finance charge}=205.16\times0.012\)

\(\text{Finance charge}=2.46\)

Second step is to calculate the New balance

\(\text{New balance}=205.16+2.46+82.10\)

\(\text{New balance}=\bold{\$289.72}\)

In conclusion, the new balance is $289.72.

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Answer: the third option, p = 2

Step-by-step explanation:

first, we move the terms around

7p - 4p = 9 - 3

then, we collect the like terms together and calculate as needed.

3p = 6

then, divide by 3 to get the variable by itself.

p = 2

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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The three Pythagorean trigonometric identities, which I’m sure one can find in any Algebra-Trigonometry textbook, are as follows:

sin² θ + cos² θ = 1

tan² θ + 1 = sec² θ

1 + cot² θ = csc² θ

where angle θ is any angle in standard position in the xy-plane.

Consistent with the definition of an identity, the above identities are true for all values of the variable, in this case angle θ, for which the functions involved are defined.

The Pythagorean Identities are so named because they are ultimately derived from a utilization of the Pythagorean Theorem, i.e., c² = a² + b², where c is the length of the hypotenuse of a right triangle and a and b are the lengths of the other two sides.

This derivation can be easily seen when considering the special case of the unit circle (r = 1). For any angle θ in standard position in the xy-plane and whose terminal side intersects the unit circle at the point (x, y), that is a distance r = 1 from the origin, we can construct a right triangle with hypotenuse c = r, with height a = y and with base b = x so that:

c² = a² + b² becomes:

r² = y² + x² = 1²

y² + x² = 1

We also know from our study of the unit circle that x = r(cos θ) = (1)(cos θ) = cos θ and y = r(sin θ) = (1)(sin θ) = sin θ; therefore, substituting, we get:

(sin θ)² + (cos θ)² = 1

1.) sin² θ + cos² θ = 1 which is the first Pythagorean Identity.

Now, if we divide through equation 1.) by cos² θ, we get the second Pythagorean Identity as follows:

(sin² θ + cos² θ)/cos² θ = 1/cos² θ

(sin² θ/cos² θ) + (cos² θ/cos² θ) = 1/cos² θ

(sin θ/cos θ)² + 1 = (1/cos θ)²

(tan θ)² + 1 = (sec θ)²

2.) tan² θ + 1 = sec² θ

Now, if we divide through equation 1.) by sin² θ, we get the third Pythagorean Identity as follows:

(sin² θ + cos² θ)/sin² θ = 1/sin² θ

(sin² θ/sin² θ) + (cos² θ/sin² θ) = 1/sin² θ

1 + (cos θ/sin θ)² = (1/sin θ)²

1 + (cot θ)² = (csc θ)²

3.) 1 + cot² θ = csc² θ

The value of the z-score for the number 15  in a data set is 0.93.

Define z-score.

A data point's z-score, also known as a standard score, indicates how far it deviates from the mean. In practical terms, however, it's a measurement of how many standard deviations a raw number is from or above the population mean.

You can plot a z-score on a normal distribution graph. Z-scores can be anywhere between -3 and +3 standard deviations.

                     ∴  z = (x – μ) / σ

Given:

σ = 4.32

x = 15

Data set: 5, 7, 9, 11, 13, 15, 17

So, mean = 5 + 7 + 9 + 11 + 13 + 15 + 17/7

                = 77/7

            μ = 11

z = (x – μ) / σ

  = (15 - 11)/4.32

   = 4/4.32

z  = 0.93

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Answer:

I got B and C.

Step-by-step explanation:

When you rotate by 180° you turn it so that it is facing the other way (ie D is B, C is A, etc) since it's a rectangle, when you rotate by 180°, you still have the same rectangle with angles in the same corners. when you reflect across the midpoint, you are just flipping your rectangle over, and so would again have the same effect as turning it 180°.

The trigonometric function that models the temperature T in the South Pole in March t hours after midnight is given as follows:

T(t) = 2cos(π/12(t - 14)) - 52.

The cosine function is defined as follows:

g(x) = acos(bx+c)+d.

The coefficients have these following roles:

The lowest temperature is of -54ºC, while the highest is of -50ºC, with a difference of 4ºC, hence the amplitude is given as follows:

2a = 4

a = 2.

A function with amplitude of 2 would oscillate between -2 and 2, while this one oscillates between -54 and -50, hence the vertical shift is given as follows:

d = -50.

The period is of 24 hours, hence:

2π/B = 24

24B = 2π

B = π/12.

The highest value of the cosine function should be assumed at t = 0, but it is assumed at t = 14(2 p.m.), hence the phase shift is given as follows:

c = 14.

Thus the function is defined as follows:

T(t) = 2cos(π/12(t - 14)) - 52.

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Using technology,  the difference between the arithmetic average ROR and the weighted average ROR is 0.52%

The Arithmetic Mean will be called the Simple Arithmetic Mean when it is calculated as the quotient between the sum of all the different related values ​​and the number of observations involved in this sum.

Given An investment portfolio

Since arithmetic average ROR:

The average arithmetic average ROR is the sum of the rate of returns divided by the number of investments arithmetic average:

ROR = (2.1%+ 4.4%+ 7.8% + 0.5%)/4

arithmetic average ROR=6.20%

total amount invested=$3200+$1750+$1235+$2,300

total amount invested=$8,485

weighted average:

ROR = (3200/8485 * 2.1%+ 1750/8485 * 4.4%+ 1235/8485 *7.8% + 2300/8485 *0.5%)

weighted average:

ROR=5.68%

difference=6.20%-5.68%

difference=0.52%

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Answer: it’s 1.1%

Step-by-step explanation: just got it right on the test

Answer:

Option 3 and 5

Step-by-step explanation:

\(\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=5\\ h=3 \end{cases}\implies V=\pi (5)^2(3)\implies V\approx 236~ft^3\)

Answer:

236 ft^3

Step-by-step explanation:

Base radius = 5 ft

Height = 3 ft

Volume =   πr^2h

              =  π × 5^2 × 3

              =  75π

               =  235.61944901923 feet^3

Nearest Cubic Foot = 236 ft^3

Nearest Cubic Foot:

Hence Answer is:

236 ft^3

Hope this helps!

The formula to calculate the mortgage payment is as follows:

Where P is the principal loan amount $325,000

i is the monthly interest rate, divide the annual interest rate by 12 to find the monthly interest rate.

n is the number of payments over the lifetime of the loan (months) then as you have a 30-year mortgage n=30 years x 12 months per year=360 payment months.

a. For 2.9% interest rate:

i=2.9%/12=0.029/12=0.002417

Replace the known values:

This would be the monthly payment when interest rate is 2.9%

b. For 2.6% interest rate:

i=2.6%/12=0.026/12=0.002167.

Thus, to calculate how much would you save over the life of the loan, multiply each monthly payment by 360 payments, and the difference would be the money you save:

Answer: You save $18591.6 over the life of the loan if the interest changed from 2.9% to 2.6%

The first 5 terms of the sequence is given by A = { -4.8 , 1.92 , -0.768 , 0.3072 , -0.12288 }

Given data ,

Let the geometric sequence be represented as A

Now , the value of A is

A = 12 ( -2/5 )ⁿ

On simplifying , we get

when n = 1

A₁ = 12 ( -2/5 ) = -4.8

A₂ = 12 ( -2/5 )²

A₂ = 12 ( 4/25 ) = 1.92

A₃ = 12 ( -2/5 )³

A₃ = -12 ( 8/125 ) = -0.768

A₄ = 12 ( -2/5 )⁴

A₄ = 12 ( 16 / 625 ) = 0.3072

A₅ = 12 ( -2/5 )⁵

A₅ = -12 ( 32 / 3,125 ) = -0.12288

Hence , the geometric sequence is solved

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Answer:

the answer is 4

Answer:

Step-by-step explanation: the y would be 50

C.) 6x^2-5x+10/x(x-2)

Answer:

62.5%

Step-by-step explanation:

Answer:

13 is the answer (GE) i hope this helped

Answer: 4.5/5 = .9 * 60 = 54, so the answer is 54 minutes.

April bought 16 kilograms of soil in total.

We need to add the amounts of soil she used for her violets and tulips. Since April used kilograms for violets and tulips, we need to convert the 3,000 grams to kilograms before we can add them up.

April bought:

9 kilograms of soil for violets

4 kilograms of soil for tulips

3 kilograms of soil for daisies (since 3,000 grams is 3 kilograms)

Therefore, April bought 16 kilograms of soil in total.

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The area of the polygon is 696

A polygon is any closed curve consisting of a set of line segments connected such that no two segments cross.

The area of a polygon is is expressed as

A = 1/2 × p × a

where p is the perimeter and a is the apothem

perimeter = n × s

where n is the number of side and s is the side length.

P = 8 × 12 = 96

A = 1/2 × 96 × 14.5

A = 1392/2

A = 696

Therefore the area of the polygon is 696

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Time that is 100% of 120 minutes is 120 minutes.

Time that is 10% of 120 minutes is 12 minutes.

Time that is 110% of 120 minutes is 132 minutes.

Percentage is the  fraction of an amount that is usually expressed as a number out of hundred. In order to convert a number as a percentage, multiply the fraction of the number by 100. The sign used to represent percentages is %. Percentages are a measure of frequency.

Time that is 100% of 120 minutes = (100 / 100) x 120 = 120 minutes

Time that is 10% of 120 minutes = (10 / 100) x 120 = 12 minutes

Time that is 110% of 120 minutes = (110 / 100) x 120 = 132 minutes

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Answer: 100% of 120 is 120 Minutes

               10% of 120 is 12 Minutes

               110% of 120 is 132 Minutes

Step-by-step explanation:

There you go!

Answer:

1:

p-r/6=-6-(-6)/6=-6+1=-5

2:

p-(m-n)= -1-(-4-4)=-1-(-8)=-1+8=7

3:

(z+y)/2)3=(-5-4)/3=-9/3=-3

4:

m/6-n=6/6-6=1-6=-5

5:

k³-h=3³-(-2)=27+2=29

6:

p-(p-(m-3))=5-(5-(4-3))=5-(5-1)=5-4=1

7:

(k)(k-j)+3=(5)(5-5)+3=5*0+3=3

8.

p²/6-q=6²/6-4=6-4=2

9;

zx+3³=6*4+3³=24+27=51.

10:

y+z-(y-x)=5+4-(5-2)=9-3=6

Some basic rules:

+. +. +=+

+. * +=+

+. ÷ +=+

+. - +=+

and

+. +. -=add and put sigh of greater one.

-. * +=-sigh

-÷-=+sigh

- - -=add and put - sigh

Answer:

-1

Step-by-step explanation:

Simply plug in (-1) to both equations and add.

Equation 1:

2(-1)^2 = 2

3(-1) = -3

2 + -3 - 1 = -2

Equation 2:

-( - 1) = 1

Add both together:

-2 + 1 = -1

Answer:

The equation is 2x² + 3x - 1 and here f(x) is -1

Putting f(x) = -1.

\(f(x) = 2 {( - 1)}^{2} + 3( - 1) - 1\)

\(f(x) = 2 (1) - 3 - 1\)

\(f(x) = 2 - 3 - 1\)

\(f(x) = - 1 - 1\)

\(f(x) = - 2\)

For g(x) put as -1

\(g(x) = - ( - 1)\)

\(g(x) = 1\)

Last step,

-2 + 1 = -1

So, option ( a) is correct

Answer:

125

Step-by-step explanation:

120 units cost 15000.

so, 1 unit is then the 120th part of the total costs.

price of 1 unit = 15000/120 = 1500/12 = 125