14. Stewart, Angela, and Thomas each prefer a different type of
book. They read history, poetry, and science fiction. Angela
does not like poetry. Thomas does not like poetry or science
fiction. Which type of book does each person like best?

the new ratiο after decreasing 72 in the ratiο οf 7:18 is apprοximately 7:16.56.

Tο decrease 72 in the ratiο οf 7:18, we need tο determine hοw much οf the 7:18 ratiο 72 represents.

First, we need tο find the tοtal number οf parts in the ratiο 7:18. This can be fοund by adding the twο numbers in the ratiο:

7 + 18 = 25

Sο the ratiο 7:18 represents a tοtal οf 25 parts.

Next, we need tο determine hοw much οf the 25 parts 72 represents. Tο dο this, we set up a prοpοrtiοn:

x/25 = 72/1

where x is the number οf parts that 72 represents.

We can sοlve fοr x by crοss-multiplying:

x = 25 * 72 / 1

x = 1800

Sο 72 represents 1800/25 = 72 parts in the ratiο 7:18.

Tο decrease 72 in the ratiο 7:18, we need tο subtract 72 parts frοm the 18 parts in the ratiο:

18 - 72/25 = 16.56 (rοunded tο twο decimal places)

Therefοre, the new ratiο after decreasing 72 in the ratiο οf 7:18 is apprοximately 7:16.56.

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The probability of drawing a black ball from the urn, with a total of 19 balls (8 red, 5 white, and 6 black), is approximately 0.3158 or 31.58%.

To determine the probability of drawing a black ball from the urn, we need to consider the total number of balls and the number of black balls.

In this case, the total number of balls in the urn is 8 + 5 + 6 = 19, as there are 8 red, 5 white, and 6 black balls.

The probability of drawing a black ball can be calculated by dividing the number of black balls by the total number of balls:

Probability = Number of black balls / Total number of balls = 6 / 19 ≈ 0.3158 (rounded to four decimal places)

Therefore, the probability of drawing a black ball from the urn is approximately 0.3158, or 31.58%.

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Answer:

A, C, E, and F

Step-by-step explanation:

They all equal \(x=2,-3\)

Answer:

A, C, E

Step-by-step explanation:

Photo is attached

A cone with a diameter of 16 centimeters has a volume of 320π cubic centimeters, the height of the cone is 15 cm.

A cone should be emptied at a time after being filled with water. The cylinder is filled to a third with each cone. Since there are three of them, the cylinder will be filled. As a result, the volume of a cone is equal to one-third of the volume of a cylinder.

Cone volume is calculated using the method V=1/3πhr².

Given that,

diameter(d) = 16 cm

radius (r) = d/2 = 8 cm

volume = 320π cubic centimeters

πr²h/3 = 320π

or, [π × (8)² × h]/3 = 320π

or,  h = (3 × 320)/(8)²

or, h = 15 cm

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Answer and explanation:

Please find explanation attached

Answer:

4x + 5

Step-by-step explanation:

10x + 4 - 6x + 1

= 4x + 5

Answer:

1:1

Step-by-step explanation:

this is because they are selected at random 3/3=1

We will use the SAS (SIDE-ANGLE-SIDE) to prove that the two triangles are congruent.  This states that if two sides and the included angle in one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

First line

First column: AB is congruent to CB      Second column: Given

Second line

First column: angle ABD is congruent to angle CBD      Second column: Given

At this point we have the  SIDE-ANGLE portion of SAS.  We just need the other side.  We can see from the given angles that they both share a side...BD.

Third Line

First column: BD is congruent to BD     Second column: Reflexive property

All that is left is to state SAS.

Fourth Line

First Column:  Triangle ABD is congruent to triangle CBD     Second column: SAS (from lines 1,2,3)

The common ratio of the resulting sequence is 1.4.

Given that, the three terms are 60, 100 and 180.

A geometric sequence is a special type of sequence where the ratio of every two successive terms is a constant. This ratio is known as a common ratio of the geometric sequence.

Let the same constant is added to the given number is x.

60+x, 100+x and 180+x

Now, the common ratio is

(100+x)/(60+x) = (180+x)/(100+x)

⇒ (100+x)(100+x)=(180+x)(60+x)

⇒ (100+x)²=10800+180x+60x+x²

⇒ 10000+200x+x²=10800+180x+60x+x²

⇒ 10000+200x=10800+180x

⇒ 20x=800

⇒ x=40

The three number are 100, 140 and 220

The common ratio is 140/100 =1.4

Therefore, the common ratio of the resulting sequence is 1.4.

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Answer:

20.2

Step-by-step explanation:

because its 20.2 trust

plz mark brainliest

If the area of the square is 36 square units. Then the area of the circle will be 28.26 square units.

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

The area of the square will be given as 36 square units.

Then the side length of the square will be

36 = a²

 a = 6 units

Then the diameter of the circle and side length of the square are equal. Then we have

a = d = 6 units

Then the radius of the circle will be

2r = d

2r = 6

 r = 3 units

Then the area of the circle will be

Area of circle = πr²

Area of circle = 3.14 x 3²

Area of circle = 28.26 square units.

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Answer:

Step-by-step explanation:

The circumference of a circle is given by the formula:

C = πd

where d is the diameter of the circle. In this case, the diameter is given as 14 cm, so we can substitute that into the formula:

C = π(14 cm)

Multiplying, we get:

C = 14π cm

So the circumference of the circle is 14π cm. The units are centimeters, since circumference is a length measurement.

Answer:

5^2

Step-by-step explanation:

For example:

a circle has 10 unit of radius, its area is pi10^2 = 314.16

then we dilate the radius by multiply by 5 is 50, pi50^2 = 7853.98

7853.98 ÷ 314.16 = 25

and 25 is equal to 5^2

a) The distance from point P to the pole  is: 6.2 m

b) The height of the Pole is: 6.2 m

The triangle attached shows us the triangle formed as a result of the given word problem about angle of elevation and distance and height.

Now, we are given that:

The angle of elevation of the top of the pole =  45°

Angle of elevation of the top of the pole = 58°.

|PQ|= 10m

a) PR is distance from point P to the pole and using trigonometric ratios, gives us:

PR/sin 58 = 10/sin(180 - 58 - 45)

PR/sin 58 = 10/sin 77

PR = (10 * sin 58)/sin 77

PR = 8.7 m

b) P O can be calculated with trigonometric ratios as:

P O = PR * cos 45

P O = 8.7 * 0.7071

P O = 6.2 m

Now, the two sides of the isosceles triangle formed are equal and as such:

R O = P O

Thus, height of pole R O = 6.2 m

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Step-by-step explanation:

y=x-2....eqn1

x+y=12.....eqn2

now,

from eqn 1

y= x-2

again, putting value of y in eqn 2

in eqn 1

hope it helps..

For the given equation:

m = 3b

The constant of proportionality is 3, so the correct option is A.

After a small search on the internet, I've found that this question asks for the constant of proportionality.

Remember that a proportional relation is of the form:

y = k*x

Where k is the constant of proportionality, and x and y are the variables.

Here the relation is:

m = 3*b

Where m and b are the variables, then the remaining coefficient is the constant of proportionality, which is 3.

In this way, we can see that the correct option is A.

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Given,

The expression of the function is,

Required

The graph of the function.

Take x = 1 then the value of y is,

Take x = 2 then the value of y is,

Take x = 0 then the value of y is,

Take x = -1 then the value of y is,

Take x = -2 then the value of y is,

The graph of the function is,

The vertex of the graph is (-2, -1).

The x - intercept of the graph is -1 and -3.

The y - intercept of the graph is at 3.

Hence, the graph of the function is obtained.

Answer:

\(\begin{array}{cc}{Status} & {Probability} & {1} & {0.0845} & {2} & {0.1127} & {3} & {0.1870} & {4} & {0.1927}& {5} & {0.4231} \ \end{array}\)

Step-by-step explanation:

Given

The above table

Required

The discrete probability distribution

The probability of each is calculated as:

\(Pr = \frac{Frequency}{Total}\)

Where:

\(Total = 2140+ 2853 + 4734 + 4880 + 10715\)

\(Total = 25322\)

So, we have:

\(P(1) = \frac{2140}{25322} = 0.0845\)

\(P(2) = \frac{2853}{25322} = 0.1127\)

\(P(3) = \frac{4734}{25322} = 0.1870\)

\(P(4) = \frac{4880}{25322} = 0.1927\)

\(P(5) = \frac{10715}{25322} = 0.4231\)

So, the discrete probability distribution is:

\(\begin{array}{cc}{Status} & {Probability} & {1} & {0.0845} & {2} & {0.1127} & {3} & {0.1870} & {4} & {0.1927}& {5} & {0.4231} \ \end{array}\)

Answer:

A'(4,-8)

B'(9,2)

C'(-7,6)

D'(-2,-3)

Step-by-step explanation:

we have to change the sign of y in reflection on x-axis and sign of X in reflection on y-axis

Answer:

Step-by-step explanation:

x² + 5x - 24

To factorize first write 5x as a difference so that when subtracted will give you 5 and when multiplied will give you - 24

That's

x² + 8x - 3x - 24

Factorize x out

That's

x( x + 8) - 3(x + 8)

Factor x + 8 out

We have the final answer as

Hope this helps you

Answer:(x-3)(x+8)

Step-by-step explanation:

The number of counters is an illustration of a linear function

The number of counters is given as:

Count = 128

Each counter is two-colored (i.e. 1/2 yellow and 1/2 red)

So, the equation that represents the number of counters that land on yellow is:

\(f(n) = 128 - \frac 12n\\\)

When one yellow side is up, we have:

f(n) = 1

So, we have:

\(1 = 128 - \frac 12*n\)

Subtract 128 from both sides

\(-127 = - \frac 12*n\)

Multiply both sides by -2

\(n =254\)

Hence, the student needs 254 trials to have one yellow side up

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The third candle is appropriate because it burns just 0.3 inches in an hour, which is significantly less than the previous candles.

The unitary procedure is a method of resolving issues that entails first figuring out the price of a single unit, then multiplication that value to figure out the needed value. Simply put, the unit technique is employed to extract a single property value from a multiple that is supplied.  This procedure could follow a regular procedure. a single nation. anything has a distinct identity. Its adjoint and reciprocal are equal in terms of mathematics, algebra, linear algebra, mathematics, or mathematical skills of matrices or operators.

given

For two hours, the first candle is 12 inches high.

12 divided by 60 equals 6 inches in an hour.

Second candle is 6 inches tall and burns for 6 hours.

Thus, 1 hour equals 6/6, or 1 inch per hour.

For 8 hours, the third candle is 3 inches tall.

1 hour equals 3/8, or 0.3 inches per hour.

The third candle is appropriate because it burns just 0.3 inches in an hour, which is significantly less than the previous candles.

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Answer:

5/18, 13/18

Step-by-step explanation:

The basic probability of anything is Specific Outcome / Total Outcomes

The specific outcome here is pulling a purple marble. We see there are 5 purple marbles therefore there are 5 ways to get them. The total outcomes are the total number of marbles which is 18. Therefore, the answer is 5/18

The complement of a probability is 1 minus the original probability, so, it would be 1 - 5/18 here getting us 13/18 as the answer.

35 people who attended the seminar of these random samples qualifies as a representative sample if studying the opinion of the attendees to a business seminar.

What does "random sample" actually mean?

A subset of a population is chosen at random in a basic random sampling.

                This sampling technique minimizes the possibility of selection bias by giving every member of the population an exact equal probability of being chosen.

Why is a random sample important? What is it?

The use of random sampling assures that the results of your study should be close to those that would have been obtained from measurements of the complete population (Shadish et al., 2002).

                        The most basic random sample gives each unit in the population an equal probability of being chosen.

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Using the Pythagoras theorem, the longest leg has the length of 24 feet.

Given that,

A ladder of length (2x+6) feet is positioned x feet from a wall.

Height of the ladder = (2x + 6) feet

Distance of ladder from the wall = x feet

Height of the wall that the ladder is placed = (2x + 4) feet

These three lengths form s right triangle where (2x + 6) feet is the hypotenuse.

Longest leg is (2x + 4) feet

Using the Pythagoras theorem,

(2x + 6)² = (2x + 4)² + x²

4x² + 24x + 36 = 4x² + 16x + 16 + x²

4x² + 24x + 36 = 5x² + 16x + 16

x² - 8x - 20 = 0

(x - 10) (x + 2) = 0

x = 10 or x = -2

x = 2 is not possible.

So x = 10

Longest leg = 2x + 4 = 20 + 4 = 24 feet

Hence the length of the longest leg is 24 feet.

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Answer:

2. Parallel (Interior Alternate Angles)

3. Not enough information

Step-by-step explanation:

For the first question, combine 60+25 which equal to 85°

Since both are 85° for interior alternate angles, the theorem states that if both interior alternate angles have same value, both lines are parallel.

Hence, both lines are parallel.

For the second question, there's not enough information. Some people may think that, "Can't we use 82-x=120"? The answer is no. 82-x=120 only applies when both lines are parallel. When we have to prove parallel lines, we cannot assume that they are parallel.

So 82-x = 120 is not valid.

Any other theorems do not work because not enough information.

Therefore, there's no enough information.