A group of entomologists has determined that the population of ladybugs at a local park can be modeled by the equation y = − 1.437 x + 197.686 , where x represents the number of years since 2010 and y represents the number of ladybugs, in thousands.
a) Predict the ladybug population at the park in 2024.
b) Predict the ladybug population at the park in 2060.

Answer:

73.5 kJ

Step-by-step explanation:

Mass of butane = 185 g

Heat of vaporization for butane = 23.1 kJ/mol

Molar mass of butane = 58.12 g/mol

Number of moles of butane = [tex]\frac{\text{Mass of butane}}{\text{Molar mass of butane}}=\frac{185}{58.12}=3.18\ moles[/tex]

Energy required for burning 185 g of butane = 3.18×23.1 = 73.5 kJ

∴ Energy is required to vaporize 185 g of butane at its boiling point is 73.5 kJ

Answer:

  A.  1 real root and 2 complex roots

Step-by-step explanation:

The one sign change among the coefficients tells you there is one positive real root. The rule of signs is inconclusive regarding the number of negative real roots. A graph shows there are none, so there are ...

  1 real root and 2 complex roots

The given polynomial F(X)=x3+4x2-16 can have either 3 real roots and 0 complex roots if the discriminant is greater than zero, or 1 real root and 2 complex roots if the discriminant is less than zero. The standard cubic formulas or numeric methods can be used to solve it.

The subject of your question is the roots of a cubic polynomial, a topic in mathematics. The given polynomial is not a quadratic equation, so the quadratic formula is not directly applicable. The roots of the polynomial F(X)=x3+4x2-16 can be complex or real numbers depending on the discriminant of the polynomial. If the discriminant of the polynomial is greater than zero, then there are 3 real roots and 0 complex roots, and if it is less than zero, there are 1 real root and 2 complex roots. Standard cubic formulas or numeric methods can be used to solve it, which is a more advanced topic usually covered in high school or college level algebra.

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Answer:

=20s³+50s²+32s+6

Step-by-step explanation:

We multiply each of the term in the initial expression by the the second expression as follows:

4s(5s²+10s+3)+2(5s²+10s+3)

=20s³+40s²+12s+10s²+20s+6

Collect like terms together.

=20s³+50s²+32s+6

Answer: It's the same thing as multiplication.

Step-by-step explanation:

Answer:

Correct arrangement of equation of displacement to find a is as follows;

1-  Vt - d = 1/2 a t^2 (^ represents exponent i.e. t square as given in equation)

2- 2(Vt - d ) = a t^2

3- a = 2(Vt - d )/ t^2   (keep in mind, 2(Vt - d) whole divided by  t^2)

Step-by-step explanation:

1-  In the first equation, Vt is taken to the left side of the equation (keep in mind, original equation of displacement used for reference as given in question) and multiplied by -1 on the both sides of the equation.

2- In the second equation, 2 is multiplied on the both sides.

3- Multiply t^2 on both sides of the equation, We will get a in correct arrangement, which is required to find.

Final answer:

The probability that Alice wins the coin-flipping game is 2/3, or approximately 66.67%. This is calculated by summing the infinite geometric series of her winning probabilities over multiple rounds.

Explanation:

The student has asked about the probability that Alice wins a coin-flipping game against Bob where Alice needs a heads to win, and Bob requires a tails to win. Each has a turn to flip the coin if the previous person does not win.

Probability is the measure of the likelihood that an event will occur. To calculate Alice's probability of winning, we consider that she has the first opportunity to win with a 50% chance (heads). If she does not get heads, Bob has a turn, also with a 50% chance (tails), but this does not directly affect Alice's probability. What affects Alice's chances are the subsequent rounds where she will have another opportunity to flip the coin if Bob does not win on his turn.

To calculate her total probability of winning, we can sum up the probabilities of her winning on the first turn, plus the probability of her winning after each complete set of turns:

Alice's probability of winning on the first turn is simply 0.5 (50% for getting heads).

If both fail their first attempt, the game starts over with the same conditions, so the probability of Alice winning on the second set of turns is (0.5 x 0.5 x 0.5), since both need to fail their first flip (0.5 x 0.5) and then Alice must succeed on her second try (x 0.5).

This pattern continues indefinitely, with each complete set of turns reducing Alice's additional chance of victory by a factor of (0.5 x 0.5).

Thus, the sum of this geometric series gives us the total probability of Alice winning:

P(Alice) = 0.5 + ([tex](0.5^3[/tex]x[tex]0.5^5)[/tex] + ... = 0.5 / (1 - (0.5^2)) = 0.5 / (0.75) = 2/3

Alice has a 2/3 (approximately 66.67%) chance of winning the game.

The value of the missing angle x° in the diagram is: 63°

By the concept of opposite angles, we know that opposite angles are defined as the angles directly opposite each other where two lines cross.

Thus:

∠ACB = 63°

Similarly, we can say that:

x° = 63°

This is because angle x is also an opposite angles to ∠ACB from the given diagram

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Answer:

128/3 cubic inches

Step-by-step explanation:

The formula for pyramid volume is (1/3)lwh. Using this we can calculate that the volume of each shape is 320/3 cubic inches and 192/3 inches. When these are subtracted, it reads 128/3 cubic inches.

Answer:

The answer is 42.67 cubic inches.

Step-by-step explanation:

Both the models are in the shape of a square pyramid.

The length of the sides of the base for both the models is 8 inches.

Amy’s model is 5 inches tall and Alex’s model is 3 inches tall.

The volume is given by :

[tex]a^{2}\frac{h}{3}[/tex]

So, Amy's figure volume is :

[tex]8^{2}\times \frac{5}{3}[/tex] = 106.67 cubic inches

And Alex's figure volume is:

[tex]8^{2}\times \frac{3}{3}[/tex] = 64 cubic inches

So, the difference between volumes is = [tex]106.66-64=42.67[/tex] cubic inches.

The answer is 42.67 cubic inches.

Answer:

  Obtuse

Step-by-step explanation:

The sum of squares of the short sides is 130, so is less than the square of the long side. The long side (12) is longer than it would need to be for a right triangle, so the largest angle is bigger than 90°.

The triangle is obtuse.

_____

A triangle solver app or calculator can confirm this. Note angle C is about 96°, an obtuse angle.

[tex]\text{lcm}(a,b)=\dfrac{|a\cdot b|}{\text{gcd}(a,b)}\\\\378=\dfrac{|a\cdot b|}{9}\\\\|a\cdot b|=42\\\\a\cdot b=-42 \vee a\cdot b=42[/tex]

So, the least value is -42

Answer:

The ratio of the reaming apples to peaches is 3 : 4

Step-by-step explanation:

* Lets solve the problem

- There are 300 apples and peaches

- The ratio of the number of apples to the number of peaches is 7 : 8

- To find the the numbers of apples and peaches add the terms of the

  ratio and then divide the total number of apples and peaches by this

  sum and then multiply each terms of the ratio by this quotient

∵ The ratio of apples to peaches = 7 : 8

∴ apple : peach : sum

      7     :     8    :    15

       ?    :       ?    :    300

∴ The number of apples = (300 ÷ 15) × 7 = 20 × 7 = 140 apples

∴ The number of peaches = (300 ÷ 15) × 8 = 20 × 8 = 160 peaches

- 50 apples and 40 peaches are sold

∴ The remaining number of apples = 140 - 50 = 90 apples

∴ The remaining numbers of peaches = 160 - 40 = 120 peaches

- To find the ratio simplify the numbers to its simplest form

∵ There are 90 apples and 120 peaches

∴ apple : peach

      90  :   120      ⇒ divided both by 10

∴       9  :    12       ⇒ divide both by 3

∴       3  :     4    

∴ The ratio of the reaming apples to peaches is 3 : 4

Step-by-step explanation:

1 can is to 10 liters as x cans is to 35 liters.

Write a proportion:

1 / 10 = x / 35

Cross multiply:

10x = 35

Divide:

x = 3.5

It takes 3.5 cans.

For this case we must build a quotient that, when multiplied by the divisor, eliminates the terms of the dividend until reaching the remainder.

It must be fulfilled that:

Dividend = Quotient * Divider + Remainder

Looking at the attached image we have that the quotient is given by:

[tex]x ^ 2 + 7x + 2[/tex]

Answer:

Option C

Answer:

  cos(θ) = -3/5

Step-by-step explanation:

The cosine of the reference angle (in the first quadrant) is ...

  cos(θ) = √(1 -sin(θ)²) = √(1 -(4/5)²) = √(1 -16/25) = √((25-16)/25)

  = √(9/25) = 3/5 . . . . in the first quadrant

In the second quadrant, the cosine is negative, so the answer is ...

  cos(θ) = -3/5

There are three ways to buy 66 cookies with packaging options of single cookies, or packages of 11 or 33. They are two packages of 33, six packages of 11, or sixty-six single cookies.

To find out how many ways you can buy 66 cookies using single cookies, or packages of 11 or 33, we can set up a problem using combinations of these quantities. As we know, 66 is a multiple of both 11 and 33, so we'll want to find out how many packages of 11 and how many packages of 33 can be combined without exceeding 66.

Firstly, since 33 is exactly half of 66, we can have either two packages of 33 or zero packages of 33. If we choose two packages of 33, then we have no need for additional cookies. If we choose zero packages of 33, we can then use six packages of 11 to make up the total because 6 x 11 = 66. There's also the option of buying 66 single cookies, although that tends to be inefficient.

So, our possibilities are:

Thus, there are three ways to buy 66 cookies given the packaging constraints.

Answer:

  10^2 . . . . see below for additional information or versions of the answer(s)

Step-by-step explanation:

You seem to want 10^exponent, where exponent is an even single digit, not zero.

We choose exponent = 2, so your expression is ...

  10^2

__

There are several versions of expanded form. One uses exponents. In that form, the expression above is the expanded form.

Another uses multipliers of 1, 10, 100, 1000, and so on. In that form, the expression expands as ...

  10^2 = 1×100

Another expanded form uses individual digits of the expanded form with others set to zero

  10^2 = 100

The standard form is ...

  10^2 = 100.

_____

We suppose your exponential expression might have another multiplier, such as 2.98:

To write an exponential expression with a base of 10 and an even exponent between 1 and 10, we can use 10^2 as an example. By multiplying the base by itself the number of times indicated by the exponent, we find that the expanded form is 10 × 10 = 100. Therefore, the standard form of the expression is 100.

a) The exponential expression with a base of 10 and an even number between 1 and 10 as the exponent would be:

102

b) To write the expression in expanded form, we would multiply the base (10) by itself the number of times indicated by the exponent (2):

10 × 10 = 100

The standard form of the expression would be 100.

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The square root property seems to be another name for completing the square

x^2 + 5x + 6 = 0

We move the constant to the other side

x^2 + 5x = -6

We square half the linear coefficient and add that to both sides

x^2 + 5x + (5/2)^2 = -6 + 25/4

Now the left side is a perfect square,

(x + 5/2)^2 = 1/4

Here's the square root property part, we take the square root of both sides, remembering the ±

x + 5/2 = ± 1/2

x = -5/2 ± 1/2

Answer: x = -3 or x=-2

We check by plugging in these values to the original equation, and they work.

------

x^2 + 6x = 16

Again we add half the linear coefficient, squared, to both sides

x^2 + 6x + 3^2 = 16 + 9

(x + 3)^2 = 25

Here comes the square root property, taking the square root of both sides:

x + 3 = ±5

x = -3 ± 5

x = 2 or x = -8

Again we check by substitution, and they both work

Answer: x = 2 or x = -8

Answer:

r=1

Step-by-step explanation:

x^2 +y^2 =1

We know that x^2 + y^2 = r^2

Replacing that in the equation

r^2 =1

Taking the square root of each side

sqrt(r^2) = sqrt(1)

r =1

The other way is to replace x with r cos theta   and y with r sin theta

(r cos theta)^2 + (r sin theta) ^2 =1

r^2 cos^2 theta + r^2 sin^2 theta = 1

Factor out r^2

r^2 (cos^2 theta + sin^2 theta) =1

We know cos^2 theta + sin^2 theta =1

r^2 (1) =1

r^2 =1

Answer:

  r = 1

Step-by-step explanation:

The usual translation between rectangular coordinates and polar coordinates is ...

Substituting these into your equation, you get ...

  (r·cos(θ))² + (r·sin(θ))² = 1

  r²(cos(θ)² +sin(θ)²) = 1 . . . . . . factor out r²

  r²(1) = 1 . . . . . . . . . . . . . . . . . . use the trig identity cos(θ)² +sin(θ)² = 1

  r = 1 . . . . . . . take the square root

_____

It's that simple. Just as x=1 describes a line in Cartesian coordinates, r=1 describes a circle in polar coordinates.

Answer:

Step-by-step explanation:

Answer:

It's C.

Step-by-step explanation:

Note. x^2 + 6x - 40 = (x + 10)(x - 4) so we have

     x - 16                    1

----------------        +  ---------

(x + 10)(x - 4)          (x + 10)

=   x - 16  + (x - 4)            2x - 20

   --------------------  =     -----------------------

    (x + 10)(x - 4)            x^2 + 4x - 40

Answer:

The area of the two-dimensional cross section is 30 feet²

Step-by-step explanation:

* Lets explain what is the right triangular prism

- The right triangular prism has five faces

- Two right triangular bases (cross sections)

- Three rectangular faces

- Its volume V = area of its base × its height

- Its surface area SA = the sum of the areas of the five faces

- The area of the triangular bases = 1/2 × base of Δ × height of Δ

* Lets solve the problem

- ABCFED is a right triangular prism

- Its two parallel bases are ABC and DEF

- Its bases are congruent right triangles

∴ AB = DE , BC = EF , AC = DF

∵ AB = 5 feet

∴ DE = 5 feet

- The two-dimensional cross section that is parallel to face ABC

  is the face DEF

∵ Δ DEF is right triangle , where angle E is a right angle

∴ DE and EF are the base and the height of Δ DEF

∵ DE = 5 feet ⇒ proved

∵ EF = 12 feet ⇒ given

∴ The area of Δ DEF = 1/2 × 5 × 12 = 30 feet²

∵ The two-dimensional cross section that is parallel to face ABC

  is the face DEF

* The area of the two-dimensional cross section is 30 feet²

Answer:

The area of the cross section is 30 feet².

Step-by-step explanation:

The area is 30, because you want to multiply 5 and 12, then multiply that by 1/2 to find the area of a right triangle.

Answer:

C.

Step-by-step explanation:

This can be written as

[tex]log_w\frac{(x^2-6)^4}{(x^2+8)^\frac{1}{3} }[/tex]

when you divide log you should subtract the terms

[tex]log_w(x^2-6)^4-log_w(x^2+8)^\frac{1}{3}[/tex]

Rewrite powers in the terms as below

[tex]4log_w(x^2-6)-\frac{1}{3} log_w(x^2+8)[/tex]

Answer:

C. [tex]4\cdot log_w(x^2-6)-\frac{1}{3}\cdot log_w((x^2+8)[/tex]

Step-by-step explanation:

We have been given an expression [tex]log_w\frac{(x^2-6)^4}{\sqrt[3]{x^2+8}}[/tex]. We are asked to choose the equivalent expression to our given expression.  

Upon applying log rule [tex]log_c(\frac{a}{b})=log_c(a)-log_c(b)[/tex], we will get:

[tex]log_w(x^2-6)^4-log_w(\sqrt[3]{x^2+8})[/tex]

Using exponent rule [tex]\sqrt[n]{x}=x^{\frac{1}{n}}[/tex], we will get:

[tex]log_w(x^2-6)^4-log_w((x^2+8)^{\frac{1}{3}}[/tex]

Now, we will apply rule [tex]log_c(a^b)=b\cdot log_c(a)[/tex] to simplify our expression as:

[tex]4\cdot log_w(x^2-6)-\frac{1}{3}\cdot log_w((x^2+8)[/tex]

Therefore, option C is the correct choice.

Answer:

1) x = 6.6.

2) x = 6.1.

Step-by-step explanation:

1) In this triangle, the hypotenuse is given, which is 8 units, and the angle is given, which is 35 degrees. The base is unknown. To find the base, following ratio will be used:

cos θ = Base/Hypotenuse.

cos 35 = x/8.

x = 8*cos 35.

x = 6.6 units (to the nearest tenth)!!!

2) In this triangle, the base is given by 12, and the angle is given by 27 degrees. The perpendicular is unknown. To find the perpendicular in this case, tangent formula will be used:

tan θ = Perpendicular/Base

tan 27 = x/12.

x = 12*tan 27.

x = 6.1 units (to the nearest tenth)!!!

Answer:

1).  x = 6.55 units

2).x = 2.55 units

Step-by-step explanation:

1). To find the value of x

From the given figure 1 we can see a right angled triangle with hypotenuse is 8 units

Cos 35 = Adjacent side/Hypotenuse

 = x/8

x = 8 * Cos 35

 = 8 * 0.8196

 = 6.55

2). To find the value of x

From the figure we can write,

Tan 27 = Opposite side/Adjacent side

 = x/12

x = 12 * Tan 27

 = 12 * 0.509

 = 2.55 units

Answer:

  20

Step-by-step explanation:

The sum of (actual - predicted) is ...

  {55, 150, 325, 510, 780, 990} - {40, 150, 300, 500, 800, 1,000}

  = total({15, 0, 25, 10, -20, -10}) = 20

The sum of residuals is 20.

The given line is y = 3x - 5 after adding Y and subtracting 5 from both sides.

The slope of this given line is 3.

Therefore, the slope of the perpendicular line is -1/3, as it must be the negative reciprocal.

The general form of a line equation in slope intercept form is y = Mx+B where M is the slope and B is the intercept.

Solving for B is: B = y- Mx

So the intercept of the perpendicular line with slope M=-1/3 and passing through (x=4, y=-3) is

y M * x

B = -3 - (-1/3)*4 =

-3 + 1/3*4 = <-- subtracting the negative is the same as adding the positive; definition of subtraction

-3 + 4/3 = <-- multiplies the fractions first per order of mixed operations

-9/3 + 4/3 <-- common denominator is 3

= -5/3

So the equation of the perpendicular line is y = -1/3X + -5/3 = -1/3X-5/3

Notice when X=4, y = -1/3(4) - 5/3 = -4/3 - 5/3 = -9/3 = -3 as expected

Answer:

3

Step-by-step explanation:

Answer:

your answer would be 4.5 cubic feet!!! HOPE I HELPED!!!!! good luck to anyone who needs this in the future

Step-by-step explanation:

The volume of the triangular prism is 44.52 cubic feet.

A prism is a three-dimensional object.

There are triangular prism and rectangular prism.

We have,

To find the volume of a triangular prism, we need to multiply the area of the base by the height of the prism.

The base of the triangular prism is a triangle with sides of lengths 2 ft, 2.5 ft, and 18 ft.

The perimeter of the base is the sum of the lengths of these sides, which is:

2 ft + 2.5 ft + 18 ft = 22.5 ft

To find the area of the base, we can use Heron's formula, which states that for a triangle with sides of lengths a, b, and c, the area is given by:

[tex]area = \sqrt{s(s-a)(s-b)(s-c)}[/tex]

where s is half the perimeter of the triangle:

s = (a + b + c) / 2

In this case, we have:

a = 2 ft, b = 2.5 ft, c = 18 ft

s = (2 ft + 2.5 ft + 18 ft) / 2

s = 11.25 ft

Plugging these values into the formula, we get:

[tex]area = \sqrt{11.25(11.25-2)(11.25-2.5)(11.25-18)}[/tex]

area = 14.84 ft^2

The volume of the triangular prism is:

volume = area of base x height

volume = 14.84 ft² x 3 ft

volume = 44.52 ft³

Thus,

The volume of the triangular prism is 44.52 cubic feet.

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Answer:

[tex]\large\boxed{\bold{Q1.}\ \overline{WX},\ \overline{XY},\ \overline{YW}}\\\boxed{\bold{Q2.}\ \angle P,\ \angle Q,\ \angle R}[/tex]

Step-by-step explanation:

The longest side is opposite the largest angle, and the shortest is opposite the smallest one.

The largest angle lies opposite the longest side, and the smallest is opposite the smallest side.

Q1.

Calculate m∠Y.

We know: Measures of angles of triangle add up to 180°.

m∠Y + m∠W + m∠X = 180°

Substitute given angles:

m∠Y + 51° + 90° = 180°

m∠Y + 141° = 180°      substitute 141° from both sides

m∠Y = 39°

39° < 51° < 90° → XW < XY < YW

Q2.

RQ < PR < PQ → ∠P < ∠Q < ∠R

Answer:

Step-by-step explanation:

The equation is y = 225 - 60x

y is the distance from Seattle

x is the number of driving hours.

At the start of the journey, x = 0.

y = 225 - 60*0

Therefore he has 225 miles to go.

====================

The change for every hour is the slope of the equation, which is - 60.

So the answer to the second part is - 60

Answer:

The distance was 225 miles when be began driving. The change in Milan's distance from Seattle for each hour he drives is -60.

Step-by-step explanation:

Consider the provided equation.

225 - 60x = y

Where x is the time and y is distance.

For part (A):

When she begins the drive, x = 0.

Substitute the value of x in the provided equation.

y = 225 - 60(0)

y = 225

Hence, the distance was 225 miles when be began driving.

Part (B)

The slope intercept form is: y = mx + c

Where m is the slope and c is the y intercept.

By comparing the provided equation with the slope intercept form it can be conclude that the slope is -60 or the rate of change of distance with respect to x is -60

The change for every hour is the slope of the equation, which is - 60.

Hence, the change in Milan's distance from Seattle for each hour he drives is -60.

Answer:

  C. None of the Above

Step-by-step explanation:

None of the given monomials have all of 4 and x and y as factors.

___

They can all be divided, but the result will be a fraction--which is probably not what is intended. None can be divided "evenly" by 4xy.

The answer is:

The line that is parallel to the given line and passes through the point (4,32) is:

[tex]y=4x+16[/tex]

To solve the problem, we need to remember that parallel lines have the same slope, so, we need to find a line that has the same slope that the given line and it also pass through the point (4,32).

So, we are given the line:

[tex]y-1=4(x+3)\\\\y=4x+12+1\\\\y=4x+13[/tex]

So, we have that the line has a slope which is equal to "4".

Now, we have to find which of the given lines that have a slope equal to "4", also pass through the point (4,32), so, we need to evaluate it into the equations.

Therefore, evaluating we have:

Third line:

[tex]y=4x-16\\\\32=4*4-16=0\\32=0[/tex]

We can see that the equation is not satisfied, so the line does not pass through the point.

So, evaluating the fourth line, we have:

[tex]y=4x+16\\\\32=4*4+16=16+16=32\\\\32=32[/tex]

We can see that the equation is satisfied, so the line does pass through the point (4,32)

Hence, we have that the line that is parallel to the given line and passes through the point (4,32) is:

[tex]y=4x+16[/tex]

Have a nice day!

Answer:

y=4x+16

Step-by-step explanation:

Let us first rearrange the equation of the given line to be in the form y=mx+c. M gives the gradient of the line and c gives the y intercept.

y-1=4(x+3)

y-1=4x+12

y=4x+13

The gradient of parallel lines is equal. For the second line m=4

m=Δy/Δx

(y-32)/(x-4)=4

y-32=4(x-4)

y-32=4x-16

y= 4x+16

The equation of line 2 will be y=4x+16

Answer: (-1.5, -0.5)

Step-by-step explanation: