The population of a pigeons in a city is 110 and is growing exponentially at 10% per
year. Write a function to represent the population of pigeons after t years, where the
quarterly rate of change can be found from a constant in the function. Round all
coefficients in the function to four decimal places. Also, determine the percentage
rate of change per quarter, to the nearest hundredth of a percent.

1st image

angle 5 is 31 degrees alternate interior angles

2nd image

angle8=angle9, alternate interior angles

Step-by-step explanation:

in order to be able to decide each case we need the slopes of all involved lines.

and that means we need to bring all of the equating into a "y = ..." form, because then the slope is always the factor of x.

parallel lines have the same slope.

the slopes of perpendicular lines (intercept at a right angle) have the y/x ratio turned upside-down and a flipped sign : -x/y.

"neither" is everything else.

our reference line

x + 2y = 6

2y = -x + 6

y = -1/2 x + 3

so, the reference slope is -1/2.

y = -1/2 x - 5 is parallel (same slope).

-2x + y = -4

y = 2x - 4 perpendicular (2/1 vs. -1/2)

-x + 2y = 2

2y = x + 2

y = 1/2 x + 1 neither

x + 2y = -2 parallel (as the structure except for the constant part is the same as our reference line).

2y = -x - 2

y = -1/2 x - 1

We have to prove (cosA−sinA+1)/(cosA-sinA-) = cotA+cosecA using Trigonometric Functions

What is Trigonometric Functions?

Trigonometry uses six fundamental trigonometric operations. Trigonometric ratios describe these operations. The sine function, cosine function, secant function, co-secant function, tangent function, and co-tangent function are the six fundamental trigonometric functions. The ratio of sides of a right-angled triangle is the basis for trigonometric functions and identities. Using trigonometric formulas, the sine, cosine, tangent, secant, and cotangent values are calculated for the perpendicular side, hypotenuse, and base of a right triangle.

L.H.S=(cosA−sinA+1)/(cosA-sinA-)

dividing by sinA

=cotA+1−cosecA/cotA−1+cosecA

​=(cotA−1+cosecA)(cotA+1+cosecA)/(cotA+1)²-cosec²A

=(cotA+cosec)²-1/2cotA

=cotA+cosecA(R.H.S)

​Hence the above trigonometric function is proved.

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The probability that a designer does not prefer red is 0.77.

Probability (event) = favorable outcome / total outcome

Total primary color designers = 400.

The number of opinions for red = 92

The probability for designer prefer red = 92 /100

The probability for designer prefer red = 0.23

Then, the probability that a designer does not prefer red = 1 - 0.23

The probability that a designer does not prefer red = 0.77

Thus, the probability that a designer does not prefer red color = 0.77.

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The correct question along with table is attached-

The length of the line segment MN given that the ratio of KL:LM:MN = 2:3:1 is; 9

We are told that the points K, L, M and N all lie on the same line segment.

Since the points lie on the same line segment, then it means that they are collinear points.

We are told that the ratio of the segments, KL:LM:MN = 2:3:1.

This means that we can find the length of MN since we are also given the total length of the whole segment, KN = 54.

Length of MN = (Individual ratio of MN ÷ the total ratio value of the 3 given segments) × length of the whole segment

Individual ratio of MN = 1

Total ratio value of the 3 given segments = 2 + 3 + 1 = 6

Length of whole segment, KN = 54

Length of MN = (1/6) * 54

Length of MN = 9

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The quadratic function has only maximum value :

[tex]F(x)_{min}[/tex] = 30

x = 3

There is no minimum value of the quadratic function.

Given,

In the question:

The quadratic function is given as:

F(x) =  [tex]-3x^2+18x +3[/tex]

Determine whether the following quadratic function has a maximum or a minimum value. Then find  the maximum and minimum value of the function.

Now, According to the question:

The quadratic function is given as:

F(x) =  [tex]-3x^2+18x +3[/tex]

Take out the leading coefficient

F(x) = -3[tex](x^2-6x)+3[/tex]

Complete the square:

F(x) = [tex]-3(x^2+(2(-3))x + (-3)^2)+(3-(-3)^2))[/tex]

Express the function in vertex form

F(x) = [tex]-3(x-3)^2+30[/tex]

To  find the maximum value

[tex]F(x)_{min}[/tex] = 30

x = 3

For Minimum value:

F(x) = [tex]-3x^2 +18x +3[/tex]

Rewrite the function by completing the square

F(x) = [tex]-3(x-3)^2+30[/tex]

The graphs always open downwards

So, There is no minimum value of the quadratic function.

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The value of x for the given parallelogram is 4.8 cm.

According to the question,

We have the following information:

We have a parallelogram with base x cm, height 2.5 cm and area 12 square centimeters.

(More to know: in a parallelogram, the opposite sides are equal and parallel to each other. Opposite angles of parallelogram are equal and the sum of consecutive angles is 180°.)

We know that the following formula is used to find the area of the parallelogram:

Area of parallelogram = Base*height

x*2.5 = 12

x = 12/2.5

x = 4.8 cm

Hence, the value of x is 4.8 cm.

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El interés junto con el préstamo de $ 200,000 tiene un monto de $ 8,080.

En este problema tenemos el caso de una persona que pide prestado $ 200,000 a una tasa de interés anual de 36 %, cuyo pago se realiza tras un plazo de dos años de realizarse el préstamo. Asumimos, que la deuda se genera por interés compuesto, esto es, un interés acumulativo. El interés compuesto es descrito mediante la siguiente fórmula:

I = C' · [(1 + r / 100)ⁿ - 1]

Donde:

Si sabemos que C' = 200,000, r = 36 y n = 2, entonces el interés a pagar al final del plazo es:

I = 200,000 · [(1 + 2 / 100)² - 1]

I = 8080

El interés a pagar es $ 8080, además del préstamo de $ 200,000.

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Answer:

D

Step-by-step explanation:

The domain of this function is all real numbers because you can see that there are no endpoints on the graph. The function is going off of the graph, which means it is continuing aka never-ending.

(-∞,∞) aka all real numbers

Answer:

60 [tex]in^{2}[/tex]

Step-by-step explanation:

Volume = the area of the base times the height.

Base:

[tex]\frac{lengthxwidth}{2}[/tex]

[tex]\frac{3x4}{2}[/tex]

6  multiply this by the height of 10

Volume = 60 [tex]in^{3}[/tex]

Answer:

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

Answer: 9

Step-by-step explanation:

        Finding the zeros is the same as solving. Then, we will add the two solutions together.

Given:

y = x² - 9x - 10

Solving by Quadradic Formula:

[tex]\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]

[tex]\displaystyle x=\frac{-(-9)\pm\sqrt{(-9)^2-4(1)(-10)} }{2(1)}[/tex]

[tex]\displaystyle x=\frac{9\pm\sqrt{81+40} }{2}[/tex]

[tex]\displaystyle x=\frac{9\pm\sqrt{121} }{2}[/tex]

[tex]\displaystyle x=\frac{9+11}{2},\;\;x=\frac{9-11}{2}[/tex]

x = 10, -1

Adding them together:

10 + -1 = 9

It is equivalent to 8^x/3

acc to our question-

to write a square root into fraction. To do that, you just have to apply the formula :

x^power/root

Then, here it gives . 8^x/3

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The value of the correlation coefficient is 0.625.

Correlation coefficients quantify the strength of a relationship between two variables. A correlation coefficient is a number ranging from -1 to 1 that indicates the degree and direction of a relationship between variables. It is a statistical notion that aids in the establishment of a relationship between predicted and actual values collected in a statistical experiment.

In this case, the slope of the model was 2.5 centimeters per pH level, and the standard deviation of the sample of plant heights was 4 centimeters.

The correlation coefficient will be:

= Slope / Standard Deviation

= 2.5 / 4

= 0.625

The coefficient is 0.625.

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The solution to the algebraic equation 8x - 8 = 4x is x = 2

Algebra: This is the system for computation using letters or other symbols to represent numbers, with rules for manipulating these symbols.

8x - 8 = 4x

8x - 4x = 8

4x = 8

x = 8/4

x = 2

Check:

8x - 8 = 4x

substitute x = 2 into the equation

8(2) - 8 = 4(2)

16 - 8 = 8

8 = 8

Other examples of algebraic equation

3x + 5 = 11

substract 5 from both sides

3x = 11 - 5

3x = 6

divide both sides by 3

x = 6/3

x = 2

Therefore, the value of x from the equation is given by 2

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The function has a maximum value of 30 at x = 3.

Given Function:

f(x) = -3[tex]x^{2}[/tex]+18x+3

here a = -3 , b = 18 , c = 3

a is negative so it has maximum value

x = -b/2a

= -18/2*(-3)

= -18/-6

= 18/6

= 3

f(x) = -3*[tex]3^2[/tex] + 18*3 + 3

= -3*9+54+3

= -27+54+3

= 27+3

= 30

Therefore the function has a maximum value of 30 at x = 3.

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Answer: [tex]x^{26}[/tex]

Step-by-step explanation:

The [tex]x^2[/tex] appears 13 times. Using the exponent rule [tex]x^a x^b=x^{a+b}[/tex], we get that:

[tex]x^2x^2x^2x^2x^2x^2x^2x^2x^2x^2x^2x^2x^2=x^{2(13)}=x^{26}[/tex]

Answer:

2 3/5

Step-by-step explanation:

First, change all terms to improper fraction

We have;

13/2÷5/2

13/2 ×2/5

13/5

Change to mixed fraction, we have;

2 3/5

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The simplest simplified form of the given expression is 3 9/10.

First, let us understand the mixed number;

A mixed number is made up of three components: a whole number, a numerator, and a denominator. The numerator and denominator are both components of the appropriate fraction that results in the mixed number.

Change all the given terms to improper fractions, we will get;

6 1/2 = (6 * 2 + 1) / 2 = 13 / 2

1 2/3 = (1 * 3 + 2) / 3 = 5 / 3

We are given;

13/2 ÷ 5/3

= 13/2 × 3/5

= 39/10

Change to mixed fraction, we will get;

39/10 = 3 9/10

Thus, the simplest simplified form of the given expression is 3 9/10.

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There are 18 students who like snickers but not twix or reese's peanut butter cups.

Given, that 500 high school students was taken to determine their favorite chocolate candy.

118 like snickers, 185 like twix, 179 like reese's peanut butter cups,

60 like snickers and twix, 87 like twix and reese's peanut butter cups, 57 like snickers and reese's peanut butter cups,

and 17 like all three kinds of chocolate candy.

Let A = Set of students like snickers

B = Set of students like twix

C = Set of students like reese's peanut butter cups

Now, we have to find the number of students like snickers but not twix or reese's peanut butter cups i.e. A - A∩B - A∩C + A∩B∩C

A - A∩B - A∩C + A∩B∩C = 118 - 60 - 57 + 17

A - A∩B - A∩C + A∩B∩C = 135 - 117

A - A∩B - A∩C + A∩B∩C = 18

Hence, there are 18 students who like snickers but not twix or reese's peanut butter cups.

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The perimeter of the rug is 37.2

The first line says that the rug is twice as long as its width. If the width is taken as w and length is taken as l, we get an equation l= 2w. Since it is a rectangle, the area of the rectangle will be (length*width) which is equal to l*w.

Since l=2w, area = 2w*w = 2w^2. This is given equally to 76.88.

2w^2 = 76.88

w^2 = 38.44

w = 6.2

l = 2w = 2*6.2 = 12.4

Now, perimeter of rectangle is 2w+2l = 2*6.2 + 2*12.4 = 37.2

Hence the perimeter of the rug is 37.2

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Answer:

y = -19.5, x = -14.5

Step-by-step explanation:

We can form equations from this statement:

x + y = -34

x - y = 5

If we rearrange the second equation, we get:

x - y = 5

x = 5 + y

Then, we substitute this value into the other equation to get the answer.

x + y = -34

5 + y + y = -34

Then solve:

2y + 5 = -34

2y = -39

so, y = -19.5

now we can find x with y:

-19.5 + x = -34

-34 + 19.5 = x

x = - 14.5

Answer:

Step-by-step explanation:

a=apples

a/7

The number 1/8 represent the fraction of full sheet of paper the teacher asked each student to color.

The information given are;

The information given are

= 1/4 of 1/2x

= 1/4 × 1/2x

= 1/8x

So therefore, the student colored 1/8 of the original piece of paper.

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Answer:

11

Step-by-step explanation:

Distance formula is square root of (x2-x1)^2+(y2-y1)^2

square root of (6-(-5))^2+(7-7)^2

square root of (11)^2+(0)^2

square root of 121+0

square root of 121

11

distance is 11

The equation of the line in the slope intercept form is y = (-1/2)x + 60

From the given graph,

Choose two points

(0, 60) and (40, 40)

The slope of the line the change in y coordinates with respect to the change in x coordinate of the function

The slope of the line = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Substitute the value in the equation

= [tex]\frac{40-60}{40-0}[/tex]

= -20/40

= -1/2

From the graph we can say that,

y intercept of the line = 60

The slope intercept form is

y = mx + b

where m is the slope of the line

b is the y intercept

y = (-1/2)x + 60

Hence, the equation of the line in the slope intercept form is y = (-1/2)x + 60

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11.5 and 15 are the values that are part of the solution set of the inequality.

Inequality is defined as relationship between non-equal numbers or expressions. The solution of an inequality is the set of values that satisfies the given inequality.

To determine the solution set of the given inequality, isolate the variable to one side and simplify.

-4x + 24 < -2x + 2

-4x + 2x < -24 + 2

-2x < -22

22 < 2x

11 < x

Hence, the solution set of the given inequality is the set of numbers greater than 11. Among the given choices, 11.5 and 15 are both greater than 11.

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Answer:

5

Step-by-step explanation:

The only way I know how to go about this is to multiply 2 until it becomes 32

2x2=4

4x2=8

8x2=16

16x2=32

Now just count how many 2 I used and I used 5 so the missing exponent is 5

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The require angle, angle ABD = 40 degrees

A bisector has two primary characteristics:

Any point along an angle's bisector is equally - spaced from the angle's sides.

The angle bisector divides the other side of a triangle in proportion to the other two sides.

Given : ∠ ABC is bisected by a ray BD

∠ ABC = 80°

Since the angle ABC is being bisected this means that the angles are equal

Let the bisected angle be x

thus we can write it mathematically as

x + x = 80

2x = 80

dividing both the sides as 2 we would get

x = 40 degrees

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