A coin (5 grams), a small parachute (21 grams), and a hammer (710 grams) are all dropped from a height of 10 meters. The coin and the hammer take
about the same amount of time to fall. Which statement describes the time it takes for the parachute to fall? (1 point)
O It takes less time to fall because it has the most surface area.
O It takes the same amount of time to fall because the effect of gravity is the same.
O It takes less time to fall because it has the least mass
O It takes longer to fall because it experiences greater air resistance.

By using concept of ratio, it can be calculated that

100 boys attended the camp

What is ratio?

Ratio between two numbers determines how much one number is greater than the other.

The first part of the ratio is called antecedent and the second part of the ratio is called consequent.

Here, concept of ratio will be used

Let the number of boys be 4x and the number of girls be 6x

There were 50 more girls than boys

By the problem,

6x - 4x = 50

2x = 50

[tex]x = \frac{50}{2}[/tex]

x = 25

Number of boys who attended the camp = 4 [tex]\times[/tex] 25 = 100

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The year for which the population of the small town is 11,511 is; Choice B; 1958.

It follows from the task content that the year for which the population of the small town in discuss becomes 11,511 be determined.

Given the function: P = 2,511 + 500t

11,511 = 2511 + 500t

9,000 = 500t

t = 9,000 / 500

t = 18 years.

Hence, the year in which case the population of the small town is; 11,511 is; 1940 + 18 = 1958.

Therefore, the year in which the population of the small town in discuss becomes 11,511 as required in the task content is Choice B; 1958 is correct.

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The function operation (f - g)(x) of the functions f(x) = -3x² + 2x - 3 and g(x) = 2x² - 3x + 4 is -5x² + 5x - 7.

A function is simply a relationship that maps one input to one output.

Given the functions in the question;

To determine the function operation (f - g)(x), replace the function designators with the real functions and simplify.

(f - g)(x) = f(x) - g(x)

(f - g)(x) = ( -3x² + 2x - 3 ) - ( 2x² - 3x + 4 )

Apply distributive property to eliminate the parenthesis.

(f - g)(x) = ( -3x² + 2x - 3 ) - ( 2x² - 3x + 4 )

(f - g)(x) = -3x² + 2x - 3 - 2x² + 3x - 4

Collect and add like terms

(f - g)(x) = -3x² - 2x² + 2x + 3x - 3 - 4

(f - g)(x) = -5x² + 5x - 7

Therefore, the function operation (f - g)(x) is -5x² + 5x - 7.

Option A is the correct answer.

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Step-by-step explanation:

x = the original number

2x + 16 = 2/5 x

multiply both sides by 5 to get rid of the fraction :

10x + 80 = 2x

divide both sides by 2 :

5x + 40 = x

subtract x from both sides :

4x + 40 = 0

divide everything by 4 :

x + 10 = 0

subtract 10 from both sides :

x = -10

Answer : x = -10

Step-by-step explanation :

x = original number

2x + 16 = 2/5x

Change 2/5 to decimal

2x + 16 = 0,4x

Change the position of 16 and 0,4x

2x - 0,4x = -1

Subtract 2 by 0,4

1,6x = -16

Divide -16 by 1,6

x = -10

You can use this way or the other one but this way is faster than the others

Hope it helps !

The sign of coordinate of x of a point after the reflection along the y-axis will be interchanged thus the coordinate of K'(2,5).

A pair of numbers that employ the horizontal and vertical distinctions from the two reference axes to represent a point's placement on a coordinate plane. typically expressed by the x-value and y-value pairs (x,y).

The given point K(-2,-5)

If we reflect a point(x,y) along the y-axis then the coordinate after reflection converts as K'(-x,y)

The reflection of K(-2,-5) along the y-axis will be  K'(2,5).

Hence "The sign of coordinate of x of a point after the reflection along the y-axis will be interchanged thus the coordinate of K'(2,5)".

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Answer:

She should choose the second cylinder-shaped box with a diameter of 30 cm and a height of 20 cm.

Step-by-step explanation:

The volume of a cylinder with a diameter of 20 cm (radius of 10 cm) and a height of 40 cm:

[tex]V=\pi{r^2h}[/tex]

[tex]V=\pi{(10^2)(40)}[/tex]

[tex]V\approx{12566.37\text{ cm}\textsuperscript{3}}[/tex]

The volume of a cylinder with a diameter of 30 cm (radius of 15 cm) and a height of 20 cm:

[tex]V=\pi{r^2h}[/tex]

[tex]V=\pi{(15^2)(20)}[/tex]

[tex]V\approx{14137.17\text{ cm}\textsuperscript{3}}[/tex]

Therefore, if Vesa wants to buy more popcorn, she should choose the second cylinder-shaped box with a diameter of 30 cm and a height of 20 cm.

The equation of the quadratic function in standard form as required in the task content is; f(x) = -x² + 12x - 43.

It follows from the task content that the standard form equation of the quadratic function is to.be determined.

Since the standard form equation can be derived from the vertex form equation as follows;

f(x) = a (x - h)² + k

f(x) = a (x - 6)² - 7

Hence, to find the value of a, Substitute x = 8 and f(x) = -11 so that we have;

-11 = a (8 - 6)² - 7

-11 = 4a - 7

4a = -4

a = -1.

Hence, the equation in vertex form is; f(x) = -1 (x -6)² - 7 and when expressed in standard form we have;

f(x) = -1(x² - 12x + 36) - 7

f(x) = -x² + 12x - 43

Therefore, the required equation in standard form is; f(x) = -x² + 12x - 43.

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The two quadratic equations are; y = x² + 2·x - 3 and y = -x² - 2·x + 3

Given,

x - intercepts = (−3,0) and (1,0).

The x-intercepts are given by the point at which the y-value of the equation are zero.

Therefore;

The quadratic equation are;

(x + 3)·(x - 1) = 0

x² + 2·x - 3 = 0

Quadratic equations;-

The polynomial equations of degree two in one variable of type f(x) = ax2 + bx + c = 0 and with a, b, c, and R R and a 0 are known as quadratic equations. It is a quadratic equation in its general form, where "a" stands for the leading coefficient and "c" for the absolute term of f. (x).

Here,

The equation can also be written in the form;

(-x - 3)·(x - 1) = 0

-x² - 2·x + 3 = 0

The quadratic equations are;

y = x² + 2·x - 3 and y = -x² - 2·x + 3

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Step-by-step explanation:

the exponential growth function is

f(t) = v0 × (1 + k)^t

1977 to 1989 is 12 years (t).

a)

so, we have

467 = 209 × (1 + k)¹²

467/209 = (1 + k)¹²

12th root(467/209) = 1 + k = 1.069295033...

k = 0.069295033...

b)

f(t) = 209 × 1.069295033...^t

c)

2009 = 32 years after 1977

f(32) = 209 × 1.069295033...³² = $1,783.478472... ≈

≈ $1,783.48

d)

double the value of 209 is 418.

418 = 209 × 1.069295033...^t

2 = 1.069295033...^t

t = log1.069295033...(2) =

= log(2)/log(1.069295033...) = 10.34554457... ≈

≈ 10.3 years

e)

2221 = 209 × 1.069295033...^t

2221/209 = 1.069295033...^t

t = log1.069295033...(2221/209) =

= log(2221/209)/log(1.069295033...) =

= 35.27452616... years ≈

≈ 35.3 years

35 years would mean end of 2012. so, 35.3 years would be early 2013.

The missing values of the ordered pairs using the given equation are:

x = -1; y = 8

The table is:

x  | y  

-3   8

-1,   2

To find the missing values of an ordered pair that satisfies a given equation, plug n the given value of one of the variables into the equation and solve to find the value of the other variable.

The equation given is y = -3x - 1

Find the missing value of the ordered pair (-3, y) by plugging in x = -3 into the equation given:

y = -3(-3) - 1

y = 8

Find the missing value of the ordered pair (x, 2) by plugging in y = 2 into the equation given:

2 = -3x - 1

2 + 1 = -3x - 1 + 1

3 = -3x

x = 3/-3

x = -1

The ordered pairs are: (-3, 8) and (-1, 2).

Therefore, we would have:

x  | y  

-3   8

-1,   2

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Step-by-step explanation:

sqrt(7) is larger than 2 (2² = 4) but smaller than 3 (as 3² is 9).

sqrt(220) is larger than 14 (14² = 196) but smaller than 15 (15² = 225).

so, the integers between them are

3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14

these are 12 integer values.

Answer:

  $920

Step-by-step explanation:

You want to know the original price of a suit on sale for $331.20, if that price represents a 64% discount.

The discounted price is found by subtracting the amount of the discount from the original price. That amount is the product of the original price and the rate of the discount.

  discounted price = price - (discount)·(price)

  discounted price = price · (1 - discount)

The the original price is ...

  price = (discounted price)/(1 - discount) = $331.20/(1 -0.64)

  price = $920

The original price of the suit was $920.00.

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The two expressions to be evaluated are

The problem asks for two expressions with positive and negative numbers

the positive numbers in the expressions are 2x and 4x

the negative numbers in the expressions are -5 and -3

At x = 5.

evaluating the first expression gives

y = 2x - 5

y = 2 * 5 - 5

y = 10 - 5

y = 5

evaluating the second expression gives

y = 4x - 3

y = 4 * 5 - 3

y = 4 * 2

y = 8

One of the expressions evaluated has error and on is error free

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1/2 - 5i/4 is the simplified form of the expression ( 5 + 2i ) / 4i.

Given the expression in the question;

( 5 + 2i ) / 4i

To simplify, multiply the numerator and denominator by the conjugate of 4i

( 5 + 2i ) / 4i

( 5 + 2i ) × i / 4i × i

( 5 + 2i )i / 4ii

Apply distributive property

( 5i + 2ii ) / 4ii

Not that i × i = i² = -1

( 5i + 2i² ) / 4i²

( 5i + 2( -1 ) ) / 4( -1 )

( 5i - 2 ) / -4

( -2 + 5i ) / -4

Split the fraction

-2/-4 + 5i/-4

1/2 - 5i/4

Therefore, the simplified form is 1/2 - 5i/4.

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Total cost of work in process Work in process inventory, ending=$1,320,000

The scenario dictates that the computation of the provided data be as follows:-

Buying raw materials will cost $1,800,000.

$20k is the opening stock of raw materials.

Raw material closing stock: $3,140,000.

Purchase of raw materials plus opening stock of raw materials minus closing stock of raw materials equals direct material used.

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Answer:

See below

Step-by-step explanation:

y = 2x+1     <====  is in form   y = mx + b   where 'm' is the slope

       ....arrange the other into this form

y = 2x-3         <===== this has the same slope as the other line

                          so the two lines are PARALLEL

The quadratic equation f(x) = - (x + 2)² + 17 represents the graph shown.

In this problem we have the definition of a quadratic equation in its vertex form, whose definition is explained below:

f(x) = a · (x - h)² + k

Where:

We need to determine the quadratic equation related to a graph shown.

First, determine the coordinates of the vertex:

(h, k) = (- 2, 17)

Second, find the vertex constant:

a = [f(x) - k] / (x - h)²

a = (13 - 17) / (0 + 2)²

a = - 4 / 4

a = - 1

Third, write the resulting function:

f(x) = - (x + 2)² + 17

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DT is congruent to TD.

A line segment is always equal to itself.

Given,

The figure;

We have to find the segments which are congruent because of the reflexive property of congruence.

Reflexive property of congruence;-

An angle, line segment, or shape is always congruent to itself, according to the reflexive characteristic of congruence in geometry. If angle A is an angle, then angle A is a congruent angle of angle A

Here,

DT = TD,

A line segment is always equal to itself.

So, DT is congruent to TD.

Congruence;-

If it is possible to superimpose one geometric figure on the other so that their entire surface coincides, that geometric figure is said to be congruent, or to be in the relation of congruence.

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With the help of substitution the answer to the equation is - (-9/2 , 5/2)

acc to our question -

Hence,The solution to the equation is (-9/2, 5/2) using substitution.

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Periods are the rows that span the periodic table. Families or groups are the columns that go from Page 2 up.

The maximal energy level of the electrons serves as a marker for the period (or row) in the periodic table that an atom belongs to (1 through 7). The table has 7 periods, hence there are 7 energy levels. The first period's atoms have electrons in the first energy level. The second period's atoms have electrons in two different energy states. The third period's atoms have electrons in three different energy levels. The fourth period's atoms have electrons in four different energy levels. Typically, the number of the period itself is the same as the number of energy levels in each period. The first period's atoms have electrons in the first energy level.

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⇒ let us first write the given equation in the form

[tex]ax^{2} +bx+c=0[/tex]

⇒[tex]49x^{2} -64=0[/tex]

⇒ Note in this case bx=0

Let us factorize the equation...49 is a square number and 64 is also a square number ..This equation is a difference of two squares which can be written as:

[tex](7x-8)(7x+8)=0[/tex]

⇒The answer is (7x-8)(7x+8)=0

The exact value of sin(θ) given that cos(θ) = -2√5/5 is √5/5

The given trigonometry ratio is

cos(θ) = -2√5/5

By the trigonometry ratio, we have

sin²(θ) + cos²(θ) = 1

Substitute cos(θ) = -2√5/5 into the above equation

So, we have the following representation

sin²(θ) + (-2√5/5)² = 1

Evaluate the exponent

sin²(θ) + 4/5 = 1

Subtract 4/5 from both sides

This gives

sin²(θ) = 1/5

Take the square root of both sides

√sin²(θ) = √1/5

Evaluate the square root

sin(θ) = ±1/√5

Sin is positive in quadrant II

So, we have

sin(θ) = 1/√5

Rationalize

sin(θ) = 1/√5 * √5/√5

This gives

sin(θ) = √5/5

This gives the value of sin(θ)

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Answer:

Domain: {0 \leq x} Range {0 \leq y}

Step-by-step explanation:

btw \leq means less than or equal to

The size of angle x in the isosceles triangle is:78°.

A triangle that has two sides that have congruent lengths is called an isosceles triangle. The base angles of the isosceles triangle are the angles that are opposite the congruent lengths, they are also equal to each other.

The triangle in the image below has two congruent sides, therefore, it is an isosceles triangle and the angles opposite its congruent sides will also be equal to each other.

Therefore:

x = 1/2(180 - 24)

x = 1/2(156)

x = 78°

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By using Pythagoras Theorem, it can be verified that

The hypotenuse of a triangle with shorter sides 1 unit each is not an integer

What is Pythagoras Theorem?

Pythagoras Theorem states that in a right angled triangle, the square of the hypotenuse is equal to the square of the sum of Perpendicular and base

According to the question given,

Shorter sides are 1 unit each

Let the length of the hypotenuse be h units

By Pythagoras Theorem,

[tex]h^2 = 1^2 + 1^2\\h^2 = 2\\h = \sqrt{2} \ units[/tex]

[tex]\sqrt{2}[/tex] is not an integer

So the hypotenuse here is not an integer.

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Answer:

Step-by-step explanation:

You want the measures of the named angles in the given figure, given c=30°.

A right angle is 90°.

A linear pair totals 180°.

Vertical angles are congruent.

Angles that make up a right angle total 90°.

Angle 'a' is marked as a right angle, so a = 90°.

Angle b is complementary to angle c, so is ...

  b + c = 90°

  b = 90° -c = 90° -30° = 60°

Angle c is given as 30°.

Angle d is part of a linear pair with angle c, so is ...

  d = 180° -30° = 150°

Angle e is a vertical angle with respect to angle c, so is congruent to it.

  e = 30°

Answer:

Step-by-step explanation:

there are fifty two cards in a deck, of which 26 are black and 26 are red, in addition there are 4 queens, including two of each color.

so:

P(getting red queen) = 2/52

P(getting black card) = 26/52

The null and alternative hypotheses for the research will be H0: µ ≥ 60 vs Ha: µ < 60

In statistical hypothesis testing, null and alternative hypotheses are utilized. A test's null hypothesis always predicts that there will be no effect or relationship between variables, whereas the alternative hypothesis outlines your research prediction of an effect or link.

A null hypothesis is a straightforward contradiction of an alternative hypothesis. This implies that if one of the two hypotheses is correct, the other is incorrect.

The null and alternative hypotheses are two claims about a population that are mutually exclusive. In this case, the hypothesis are illustrated above.

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Answer:

your question is cutoff, cant read it