Liam is setting up folding chairs for a meeting. If he arranges the chairs in 4 rows of the same length, he has 5 chairs left over. If he arranges the chairs in 2 rows of that same length, he has 17 left over. How many chairs does Liam have?

The Answer is C 5/6

250/300 reduced and simplified is 5/6

Answer:

The probability that the student is right-handed given that the student is a girl is:

[tex]\dfrac{5}{6}[/tex]

Step-by-step explanation:

From the tree diagram we have to find the probability that the students is right handed given that the student is a girl.

Let A denote the event that the student is a girl.

and B denote the event that the student is right handed.

We are asked to find the probability:

P(B|A)

We know that P(B|A) is calculated as:

[tex]P(B|A)=\dfrac{P(A\bigcap B)}{P(A)}[/tex]

There are a total of 500 students.

Out of which 300 are girls.

( i.e. [tex]P(A)=\dfrac{300}{500}=\dfrac{3}{5}[/tex]    )

and out of 300 girls 250 are right handed.

( i.e. [tex]P(A\bigcap B)=\dfrac{250}{500}=\dfrac{1}{2}[/tex]  )

Hence,

[tex]P(B|A)=\dfrac{\dfrac{1}{2}}{\dfrac{3}{5}}\\\\\\P(B|A)=\dfrac{5}{6}[/tex]

Hence,The probability that the student is right-handed given that the student is a girl is:

[tex]\dfrac{5}{6}[/tex]

Answer: [tex]\angle WXY=125^{\circ}[/tex]

Explanation: Since, a kite has one pair of congruent angles and its main diagonal bisects its opposite angles.

Therefore, According to the given figure,

[tex]\angle WXY=\angle WZY[/tex]

And, WY is the main diagonal which bisects angles ZWX and XYZ.

So, [tex]\angle ZWX =2\times \angle ZWY= 2\times 43^{\circ}=86^{\circ}[/tex]

And, [tex]\angle XYZ =2\times \angle XYW= 2\times 12^{\circ}=24^{\circ}[/tex]

Since, Sum of all angles of a quadrilateral is equal to [tex]360^{\circ}[/tex]

Therefore, [tex]\angle WXY+\angle WZY+\angle XYZ+\angle ZWX=360^{\circ}[/tex]

⇒[tex]2\times \angle WXY+ 86^{\circ}+24^{\circ}=360^{\circ}[/tex]

⇒[tex]2\times \angle WXY=360^{\circ}-110^{\circ}=250{\circ}[/tex]

⇒ [tex]\angle WXY=125^{\circ}[/tex]

When two parallel lines are cut by a transversal vertical lines are not always congruent.

A line that goes through two lines in the same plane at two different points is called a transversal. When determining whether two or more other lines in the Euclidean plane are parallel, transversals play a role. Different kinds of pairs of angles are created when two lines intersect a transversal: alternate angles, corresponding angles, consecutive exterior angles, and consecutive interior angles. If the two lines are parallel, Euclid's parallel postulate states that consecutive interior angles are supplementary, that corresponding angles are equal, and that alternate angles are equal.

Given  to find the pairs of angles are not always congruent when two parallel lines are cut by a transversal,

when parallel lines are cut by a transversal some pair of angles are congruent like alternative exterior angle, corresponding angles and  

Consecutive interior angles all the pairs are congruent and equal.

but When a transversal line cuts through two parallel lines, vertical lines are not always congruent.

Therefore vertical lines are not always congruent.

Learn more about transversal;

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Final answer:

To find the decibel rating of sound b, we calculate the decibel difference between sound a and sound b, which is 9.031 decibels. Adding this to the decibel rating of sound a gives us an approximate decibel rating of 34 for sound b.

Explanation:

To find the decibel rating of sound b, we need to determine how many decibels louder it is compared to sound a. We know that sound b is 8 times as loud as sound a, so we can use the formula for decibel difference:

Decibel difference = 10 * log10(intensity ratio)

Since sound b is 8 times as loud as sound a, the intensity ratio is 8. Plugging this into the formula gives:

Decibel difference = 10 * log10(8) = 10 * 0.9031 = 9.031 decibels

To find the decibel rating of sound b, we add the decibel difference to the decibel rating of sound a:

Decibel rating of sound b = Decibel rating of sound a + Decibel difference = 25 + 9.031 ≈ 34 decibels

12/40 =0.3

28 *0.3 = 8.4

it will cast a 8.4 foot long shadow

Answer:

The shadow cast by a 28-foot tree is 8.4 foot.

Step-by-step explanation:

The rule of three is a way of solving problems of proportionality between three known values and one unknown, establishing a relationship of proportionality between all of them. In the case of direct proportionality, when one magnitude increases, the other increases (  or if one magnitude decreases, the other will also decrease)

This is an example of application of this rule:

40 foot tree ⇒ 12 foot shadow

28 foot tree ⇒ x foot shadow

Then, to solve and calculate the value of x, which is the value of the shadow cast by the 28-foot tree, perform the count:

x=[tex]\frac{28*12}{40}[/tex]

x=[tex]\frac{336}{40}[/tex]

x=8.4

This means that the shadow cast by a 28-foot tree is 8.4 foot.

The measure of the complementary angle will be 61°.

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360 °.

Complementary angle - Two angles are said to be complementary angles if their sum is 90 degrees.

An angle measures 29°.

Let 'x' be the complementary angle. Then the measure of the complementary angle is given as,

x + 29° = 90°

Simplify the equation, then we have

x + 29° = 90°

x = 61°

The measure of the complementary angle will be 61°.

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fisher has x cars

 sawyer has 3 times as many so he has 3x cars

Answer is B

The products of two numbers involves multiplying them.

The two numbers are -5 and 6

Let the numbers be x and y.

So, we have:

[tex]\mathbf{x \times y = -30}[/tex]

[tex]\mathbf{x + y = 1}[/tex]

Make x the subject in [tex]\mathbf{x + y = 1}[/tex]

[tex]\mathbf{x = 1 - y}[/tex]

Substitute [tex]\mathbf{x = 1 - y}[/tex] in [tex]\mathbf{x \times y = -30}[/tex]

[tex]\mathbf{(1 - y)y = -30}[/tex]

Expand

[tex]\mathbf{y - y^2 = -30}[/tex]

So, we have:

[tex]\mathbf{y^2 -y - 30 = 0}[/tex]

Expand

[tex]\mathbf{y^2 -6y + 5y - 30 = 0}[/tex]

Factorize

[tex]\mathbf{y(y -6) + 5(y - 6) = 0}[/tex]

Factor out y - 6

[tex]\mathbf{(y + 5) (y - 6) = 0}[/tex]

Solve for y

[tex]\mathbf{y = -5\ and\ 6}[/tex]

Hence, the two numbers are -5 and 6

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Answer:

[tex]-7\geq x<12[/tex] and [tex][-7,12)[/tex] in interval notation.

Step-by-step explanation:

We have been given a compound inequality [tex]-7x-50\leq -1\text{ and }-6x+70>-2[/tex]. We are supposed to find the solution of our given inequality.

First of all, we will solve both inequalities separately, then we will combine both solution merging overlapping intervals.

[tex]-7x-50\leq -1[/tex]

[tex]-7x-50+50\leq -1+50[/tex]

[tex]-7x\leq 49[/tex]

Dividing by negative number, flip the inequality sign:

[tex]\frac{-7x}{-7}\geq \frac{49}{-7}[/tex]

[tex]x\geq -7[/tex]

[tex]-6x+70>-2[/tex]

[tex]-6x+70-70>-2-70[/tex]

[tex]-6x>-72[/tex]

Dividing by negative number, flip the inequality sign:

[tex]\frac{-6x}{-6}<\frac{-72}{-6}[/tex]

[tex]x<12[/tex]

Upon merging both intervals, we will get:

[tex]-7\geq x<12[/tex]

Therefore, the solution for our given inequality would be [tex]-7\geq x<12[/tex] and [tex][-7,12)[/tex] in interval notation.

Answer:

Step-by-step explanation:

Given is the polynomials as

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

The graph of this function has x intercepts as

-2, -1 and 0

Since f(x) =0 has solutions equivalent to x intercepts we see that the roots are

-2,-1 and 0

2) Given is a polynomial as

[tex]f(x) = 2x^3+5x^2-8x-20 =0[/tex]

Using rational roots theorem we find that

the roots possible are ±1.±2,±4,±5,±10,±20,±1/2,±5/2

Using remainder theorem we see that

f(2) =f(-2)=0

By using division, we find that the other factor is 2x+5

Hence roots are 2,-2, -2.5

Answers:

  A. If two angles are linear pairs, the angles are supplementary. The two angles are linear pairs. Therefore, the angles are supplementary.  

 B. If an object is a square, it is a parallelogram. The object is a square. The object is a parallelogram.

 C. If it is snowing, the play will be cancelled. It is snowing. Therefore, the play is cancelled.

  These are right.

Answer:

Law of detachment:

Statement 1: If a, then b

Statement 2: a

Conclusion: b

(A)

1. If two angles are linear pairs, then the angles are supplementary.

2. The two angles are linear pairs.

Let a be the statement " two angles are linear pairs"

let b be the statement "the angles are supplementary"

then, 1 and 2 can be written as;

1. if a , then b

2. a

So, by the law of detachment we can deduce that b is true.

i.e, The angles are supplementary.

(B)

1. If an object is a square, then it is a parallelogram.

2. The object is a square.

Let a be the statement " an object is a square"

let b be the statement "The object is a square"

then, 1 and 2 can be written as;

1. if a , then b

2. a

So, by the law of detachment we can deduce that b is true.

i.e, The object is a parallelogram.

(C)

1. If  it is snowing, then the play will be cancelled.

2. It is snowing.

Let a be the statement "it is snowing"

let b be the statement "the play will be cancelled"

then, 1 and 2 can be written as;

1. if a , then b

2. a

So, by the law of detachment we can deduce that b is true.

i.e, The play is cancelled.

Only option A, B and C  are examples of the Law of Detachment.