Vertical plane R intersects horizontal plane P. Points A, D, and B are on the line of the intersecting planes. Point F is on the top half of plane R. Point G is on the bottom half of plane G. Point C is on the left half of plane P. Point E is on the right half of plane P. Point H is above and to the right of the planes. Point J is below and to the left of the planes. Which statements are true based on the diagram? Check all that apply. Points A, B, and D are on both planes. Point H is not on plane R. Plane P contains point F. Points C, D, and A are noncollinear. The line containing points F and G is on plane R. The line containing points F and H is on plane R.

The lateral and total surface areas of the given cone are 753.98 cm² and 1206.31 cm² respectively.

A cone has a height 'h', radius 'r', and slant height 'l'.

The slant height of the cone is obtained by the Pythagorean theorem. I.e.,

l² = h² + r²

Then,

Its lateral surface area(LSA) = πr([tex]\sqrt{h^2+r^2}[/tex]) square units and

Its total surface area(TSA) = πr(r + l) square units

It is given that,

A cone has a height h = 16 cm and radius r = 12 cm

Then, the slant height is calculated by

l² = h² + r²

l  = [tex]\sqrt{h^2+r^2}[/tex]

On substituting,

l = [tex]\sqrt{16^2+12^2}[/tex]

 = [tex]\sqrt{400}[/tex]

 = 20 cm

So,

LSA = πr([tex]\sqrt{h^2+r^2}[/tex])

       = π × 12 × ([tex]\sqrt{16^2+12^2}[/tex])

       = π × 12 × 20

       = 753.98 cm²

and

TSA = πr(r + l)

       = π × 12 × (12 + 20)

       = π × 12 × 32

       = 1206.37 cm²

Therefore, the lateral and total surface areas of the cone with a height of 16 cm and a radius of 12 cm are 753.98 cm² and 1206.37 cm².

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Answer: The lateral area is 240π square centimeters. The total surface area is 384π square centimeters.

Step-by-step explanation:

The equilibrium level if autonomous expenditures are $2,000 and the mpe is 0. 5 is $4000.

From the information given, the autonomous expenditures are $2,000 and the mpe is 0. 5.

Here, the equilibrium level will be:

= 2000/(1 - 0.5)

= 2000/0.5

= 4000

In conclusion, the correct option is $4000.

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If they plan to split the cost evenly, the expression that could be used to find how much they each owe is 18/3

The given parameters are:

Total amount owed = 18 dollars

Number of friend = 3

If they plan to split the cost evenly, the expression that could be used to find how much they each owe is represented as:

Amount = Total/Friends

This gives

Amount = 18/3

Hence, the expression is 18/3

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Answer:

10

Step-by-step explanation:

It's just symmetry. You see that the geometrical construction above has been rotated, so its properties will remain the same.

Answer:

C.  All real numbers.

Step-by-step explanation:

The domain is the set of all x values that are used by points on the graph.  This is a sine wave, and we assume it extends infinitely far to the left and right.  Even without that assumption, you can eliminate the other answers.

A. This describes the numbers on the x-axis between 0 and 5, inclusive.  But the graph includes many more points with x-coordinates beyond that interval.

B. The same sort of thing: the graph extends well beyond the interval of x values between -5 and 5, inclusive.

D.  This would mean the graph has only points with positive x-coordinates, but there are many with negative (or 0) x-coordinates.

The relationship is not an inverse variation because the product xy is not a constant.

Inverse variation is the relationship between two quantities whereby an increase in one quantity cause a decrease in the other quantity.

In this type of variation the product of the two quantities is constant.

Analysis:

if x is one quantity and y is the other,

Mathematically, x = [tex]\frac{k}{y}[/tex]

Where, k is a constant,

it means k = xy

from the table, when, x =2, y = 409, xy = 2 x 409 = 818

Also, x = 3, y = 240, xy = 3 x 240 = 720

Therefore, 720 not equal to 818.

In conclusion, The product xy is not a constant, so the relationship is not an inverse variation.

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Answer:

Step-by-step explanation:

Rectangles have 2 pairs of equal sides that means:

2(4x) and 2(3x+2)

8x and 6x+4

8x+ (6x + 4) = 14x + 4

Answer:

this graph has an x-intercept values of -1 and 2

Answer:

Step-by-step explanation:

I got you  first you want to get some little ceasers

The equation of the graph is [tex]f(x) = -\sqrt{x -2[/tex]

The graph is added as an attachment

The form of the graph is

[tex]f(x) = a\sqrt{x + b[/tex]

The graph passes through the points (2, 0) and (6, -2).

So, we have:

[tex]0 = a\sqrt{2 + b[/tex] and [tex]-2 = a\sqrt{6 + b[/tex]

Solve for b in [tex]0 = a\sqrt{2 + b[/tex]

Divide both sides by a

[tex]0 = \sqrt{2 + b[/tex]

Square both sides

0 = 2 + b

Subtract 2 from both sides

b = -2

Substitute b = -2 in [tex]-2 = a\sqrt{6 + b[/tex]

[tex]-2 = a\sqrt{6 -2[/tex]

[tex]-2 = a\sqrt{4[/tex]

Evaluate the square root

-2 = 2a

Divide by 2

a = -1

Substitute b = -2 and a = -1 in [tex]f(x) = a\sqrt{x + b[/tex]

[tex]f(x) = -\sqrt{x -2[/tex]

Hence, the equation of the graph is [tex]f(x) = -\sqrt{x -2[/tex]

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The true statements are (b), (d) and (e)

From the function, we have the following piecewise function and the domains

D(t) = 300t + 125, 0 ≤ t < 2.5

D(t) = 875, 2.5 ≤ t ≤ 3.5

D(t) = 75t + 612.5, 3.5 < t ≤ 6

When t = 2, we use the domain 0 ≤ t < 2.5

So, we have

D(2) = 300 * 2 + 125

Evaluate the product

D(2) = 600 + 125

Evaluate the sum

D(2) = 725 --- this is true

When t = 3, we use the domain 2.5 ≤ t ≤ 3.5

So, we have

D(t) = 875

This gives

D(3) = 875 -- this is true

When t = 6, we use the domain 3.5 < t ≤ 6

So, we have

D(t) = 75t + 612.5

This gives

D(6) = 75* 6 + 612.5

Evaluate the product

D(6) = 450 + 612.5

Evaluate the sum

D(6) = 1062.5 --- this is true

Hence, the true statements are (b), (d) and (e)

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Complete question

Select three options. The starting distance, at 0 hours, is 300 miles. At 2 hours, the traveler is 725 miles from home. At 2.5 hours, the traveler is still moving farther from home. At 3 hours, the distance is constant, at 875 miles. The total distance from home after 6 hours is 1,062.5 miles.

Answer:

At 2 hours, the traveler is 725 miles from home.

At 3 hours, the distance is constant, at 875 miles.

The total distance from home after 6 hours is 1,062.5 miles.

Step-by-step explanation:

The examples of sinusoids include sound and water waves.

Simple harmonic motion such as that of a pendulum or a weight attached to a spring results in a sinusoidal relationship between position and time.

The angle will be formed after t time of the starting of the motion.

θ = wt = 2πt/20 = πt/10

Radius of the wheel = 30/2 = 15 feet

Distance from the ground = (15 - 15cosθ) + 8 = (15 - 15cosπt/10) + 8

= 23 - 15cos(πt/10)

As we know the minimum value of the cos is -1

-1 ≤ cos(πt/10) ≤ 1

8 ≤ 23 - 15cos(πt/10) ≤ 38

The lowest distance = 8 feet

It should be always greater than zero as the lowest point of what should be above the ground.

d = 23 - 15cos(πt/10)

Plug t = 3 in the above equation:

d(3) = 14.18 feet

For t = 8

d(8) = 35.13 feet

For t = 15

d(15) = 23 feet

For t = 19

d(19) = 8.73 feet

Thus, the lowest distance is 8 feet, and the lowest point of what should be above the ground and the equation is d = 23 - 15cos(πt/10).

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[tex]\frac{97}{100}[/tex] probability that a randomly chosen college student either has a job or lives on campus.

What is probability?

To find the probability that a randomly chosen college student either has a job or lives on campus:

Given: 85% of college students have a job, 54% live on campus, and 42% have a job and live on campus.

So, out of 100 students, 42 students either has a job or live on campus.

43 college students have a job and 12  live on campus.

So, 43 + 42 + 12 = 85 + 54 - 42

85 + 12 = 139 - 42

97 = 97

Therefore, [tex]\frac{97}{100}[/tex] probability that a randomly chosen college student either has a job or lives on campus.

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Answer:

Step-by-step explanation:

The "zero product principle" or "zero product rule" tells you a product will be zero if and only if one or more of the factors is zero. This fact is used to solve quadratic equations by factoring.

Factoring the equation y = ax² +bx +c to the form y = a(x -r)(x -s) allows you to immediately identify the solutions of y=0 as x=r and x=s. These are the values of x that make the factors zero, hence making the product zero.

Finding the values of x that satisfy ax² +bx +c = 0 by rearranging it to the form a(x -r)(x -s) = 0 is called "solving by factoring."

When the process of "completing the square" is applied to the standard-form quadratic y = ax² +bx +c, the result is a formula for the two solutions to y = 0:

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

This quadratic formula tells you the solutions based on the coefficients of the original equation, so does not require rearranging the equation in any way.

The number of ways pets can be arranged in group according to the species is  in a row 288 ways.

Pets can be grouped by permutation concept as follows.

Total number of pets = 10

Number of dogs = 4

Number of cats = 3

Number of alpacas = 2

Number of bunny = 1

The number of ways pets can be arranged in group according to the species in a row as,

⇒ (4!)(3!)(2!)(1!)

⇒ (24)(6)(2)(1)

⇒ 288

Hence we can conclude that the number of ways pets can be arranged in group according to the species in a row is 288 ways.

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4) [tex]A_{QRST} = A_{Q'R'S'T'} = 9[/tex].

5) The areas of the rectangles QRST and Q'R'S'T' are the same since the translation of the geometric loci conserved the Euclidean distance.

6) x = 1, w = 3, y = - 1/4, z = 1/3

Rigid transformations are transformations applied on geometric loci such that Euclidean distance is conserved. In this question we have applications of translations, a kind of rigid transformation.

Exercise 4

In this part we must determine the areas of rectangles QRST and Q'R'S'T':

Rectangle QRST

A = RS · QT

A = 3 · 3

A = 9

Rectangle Q'R'S'T'

Q'(x, y) = (2, - 3) + (- 3, - 3)

Q'(x, y) = (- 1, - 6)

R'(x, y) = (2, 4) + (- 3, - 3)

R'(x, y) = (- 1, 1)

S'(x, y) = (5, 4) + (- 3, - 3)

S'(x, y) = (2, 1)

T'(x, y) = (5, - 3) + (- 3, - 3)

T'(x, y) = (2, - 6)

A = R'S' · Q'T'

A = 3 · 3

A = 9

The rectangles QRST and Q'R'S'T' have both an area of 9 square units.

Exercise 5

The areas of the rectangles QRST and Q'R'S'T' are the same since the translation of the geometric loci conserved the Euclidean distance.

Exercise 6

In this case, we must solve the following equations:

PQ = A'(x, y) - A(x, y)

(4, 1) = (2 · x + 1, 4) - (- 1, w)

(4, 1) = (2 · x + 2, 4 - w)

(4, 1) = (2 · x, - w) + (2, 4)

(2, - 3) = (2 · x, - w)

(x, w) = (1, 3)

PQ = B'(x, y) - B(x, y)

(4, 1) = (3, 3 · z) - (8 · y - 1, 1)

(4, 1) = (2 - 8 · y, 3 · z)

(4, 1) = (- 8 · y, 3 · z) + (2, 0)

(2, 1) = (- 8 · y, 3 · z)

(y, z) = (- 1/4, 1/3)

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The area of the triangle abc in which bd is altitude and having coordinates a(-6,0),b(0,0),c(0,6),d(3,-3) is 18 square units.

Given the coordinates of abcd are a (-6,0) b (0,0) c (o,6) and d (3,-3).

We are required to find the area of the triangle when bd is the altitude of the triangle.

When we draw the triangle we will find that that the base is ac and altitude is given bd.

ac=[tex]\sqrt{(6-0)^{2} +(0+6)^{2} }[/tex]

=[tex]\sqrt{36+36}[/tex]

=[tex]\sqrt{72}[/tex]

=6[tex]\sqrt{2}[/tex]

bd=[tex]\sqrt{(-3-0)^{2} +(3-0)^{2} }[/tex]

=[tex]\sqrt{9+9}[/tex]

=[tex]\sqrt{18}[/tex]

=3[tex]\sqrt{2}[/tex]

Area=(Base*Height)/2

=(6[tex]\sqrt{2}[/tex]*3[tex]\sqrt{2}[/tex])/2

=(18*2)/2

=18 square units.

Hence the area of the triangle abc in which bd is altitude and having coordinates a(-6,0),b(0,0),c(0,6),d(3,-3) is 18 square units.

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Answer:

  24

Step-by-step explanation:

The semi-axis lengths are 'a' and 'b' in the equation ...

  (y -k)²/a² -(x -h)²/b² = 1

The area of the central rectangle will be ...

  A = LW

The axis lengths are 2a and 2b, so the area is ...

  A = (2a)(2b) = 4ab

In terms of the numbers in the given equation, this is ...

  A = 4√(a²b²) = 4√(3×12)

  A = 4×6 = 24

The area of the central rectangle is 24 square units.

Answer:

x = 8

Step-by-step explanation:

complementary angles sum to 90°

sum the 2 angles and equate to 90

5x + 50 = 90 ( subtract 50 from both sides )

5x = 40 ( divide both sides by 5 )

x = 8

The recursive formula for the geometric sequence is given as follows:

D.

A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.

The nth term of a geometric sequence is given by:

[tex]a_n = a_1q^{n-1}[/tex]

In which [tex]a_1[/tex] is the first term.

With a recursive formula, it is given by:

[tex]a_n = a_{n-1} \times q[/tex]

For this problem, the first term and the common ratio are:

[tex]a_1 = 9, q = -\frac{1}{3}[/tex]

Then the recursive formula is:

D.

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During the month of May, there were 130 births, of which the newborn death rate is 38.4615.

According to the question,

There were 130 births, of which 127 were full-term births and three were premature births. There were five newborn deaths.

In order to find the newborn death rate we have the formula:

=  [tex]\frac{number of death under 28 days of age }{Total live births in the same year}[/tex]  × 1000

= [tex]\frac{5}{130}[/tex] × 1000

=[tex]\frac{5000}{130}[/tex]

=38.4615

Hence, the new born death rate is 38.4615.

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The primary goal of a data scientist is to create new questions using data.

In the data ecosystem, a data scientist is one who creates new questions using data.

Unlike a data scientist, a data analyst uses existing data questions to find answers through insightful analysis of data.

Data designers design databases and database-specific constructs, and the procedures for storing, retrieving, and deleting persistent objects.

Data engineers build data systems to collect, manage, and convert data into information for both data scientists and analysts.

Thus, the primary goal of a data scientist is to create new questions using data.

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a) scientist

b) engineer

c) designer

d) analyst

The perimeter of the rectangle that has a length of 5 3/5 inches, and the width as half of its length is 16.8 inches. Hence, option A is the right choice.

The perimeter of any object is the total sum length of its boundary.

The perimeter of a rectangle with length l units and width w units is given as:

Perimeter = 2(l + w) units.

In the question, we are given that the length of a rectangle is 5 3/5 inches and its width is half of its length. We are asked to find the perimeter of the rectangle.

The length of the given rectangle (l) = 5 3/5 inches = 28/5 inches.

The width of the given rectangle (w) = Half of length = 1/2 * 28/5 inches = 14/5 inches.

Thus, the perimeter of the rectangle = 2(l + b) = 2(28/5 + 14/5) inches,

or, the perimeter = 2(42/5) inches,

or, the perimeter = 84/5 inches,

or, the perimeter = 16.8 inches.

Thus, the perimeter of the rectangle that has a length of 5 3/5 inches, and the width as half of its length is 16.8 inches. Hence, option A is the right choice.

The given question is incorrect. The correct question is:

"The length of a rectangle is 5 3/5 inches. the width of the rectangle is half of its length. what is the perimeter of the rectangle?

(a) 16.8 inches

(b) 8.4 inches

(c) 2.8 inches

(d) 15.68"

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[tex]\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: {\large{\textsf{\textbf{\underline{\underline{Answer : \:}}}}}}[/tex]

False, because the number 40 is a composite number, those that cannot be broken down are called Prime Numbers.

Prime numbers are numbers that are used to decompose any number, but prime numbers cannot be decomposed, since they only have two Divisors, which are 1 and itself.

[tex]~\sf{Atte: Murdock:)}[/tex]

Answer: False

Step-by-step explanation:

All whole numbers can be decomposed into prime factors. For the number 40, the prime factorization would be [tex]2 * 2 * 2*5[/tex]. Since all 4 of those numbers are prime numbers, the answer is false.

Answer:

y=3x+4

Step-by-step explanation:

The original formula for slope-intercept is y=mx+b.

b is your y-intercept (where the line crosses the y-axis).

m is your slope which is 3/1 or just 3.

Answer: Read the explanation

Step-by-step explanation:

If the points of a figure are all moved the same, they are congruent.

Point A is moved 9 points right, and 7 points down.

Point B is moved 9 points right, and 7 points down.

Point C is moved 9 points right, and 7 points down.

So, they are congruent.

AB will be an Identity matrix.

As it is given in the description itself, if the answer to a matrix multiplication problem is an identity matrix, then each of the two matrices is an inverse matrix of the other.

Therefore, AB will be an Identity matrix.

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Answer:

AB= I

ABA=A

BBA=B

BBAA=I

Step-by-step explanation:

just took the test on edge. 2022

Answer :

( 6 y^4 + 3 y^2 -7) - (12 y^4 - y^2 + 5)

Step-by-step explanation:

(6 y^4+ 3 y^2-7) - (12 y^4 - y^2 + 5 )

=6 y^4 +3 y ^2 - 7 - 12 y^4 + y^2 - 5

=6 y ^4 - 12 y ^4 +3 y ^2 + y ^2 - 7 -5

= -6 y ^4 + 4 y ^2- 12

Hope this helps!