Triangle RST and triangle XYZ are shown.
Based on the diagrams, which information is true for triangle RST and triangle XYZ?

a. The measure of R is congruent to Y, and the measure of S is congruent to Z. If two angles in one triangle are congruent to two angles in another triangle, then the third pair of angles are also congruent. Therefore, RST and XYZ are not similar because the sides appear to be different lengths.

b. The measure of R is congruent to Y, and the measure of S is congruent to Z. If two angles in one triangle are congruent to two angles in another triangle, then the third pair of angles are also congruent. Therefore, RST and XYZ are similar.

c. RST and XYZ are similar because they have two pairs of congruent angles and the lengths of the sides are different.

d. RST and XYZ are not similar because although two pairs of angles are congruent, the third pair does not have to be congruent.

60 engineering students are divided into 24 who take math and 29 who take physics. 10 students take statistics and physics together, 13 students take math and physics together. a) There are 26 students take statistics. b) P(A/B)=4/13.

The science of statistics is concerned with the research and advancement of methods for collecting, analyzing, interpreting, and presenting empirical data. The science of learning from data is called statistics, which is also possibly an art. The discipline's focus is on the gathering, analyzing, and interpretation of data as well as the efficient dissemination and presentation of findings that rely on data.

We can assume the following:

1). There are 13-8=5 pupils who study physics and math together but not statistics (green colour)

2). There are 10-8=2 pupils who study physics and statistics together but not math (grey colour)

3). Students who take algebra and statistics but not physics total 11-8=3. (yellow colour)

4). There are 14 pupils (29-5-8-2) who only take physics (pink colour)

We can now determine how many students solely take statistics by doing the following: The number of students enrolled in at least one course (60–7) less the number taking only math or just physics or just statistics but not math.

53-24-14-2=13 students take only statistics

There are 26 students who take statistics, or 13 + 2 + 3 + 8

b) Let's say A takes all three, and B takes statistics. Finding conditional probability is the goal.

P(A/B)= P(A⋂B)/P(B)

P(A⋂B)= 8/60, P(B)=26/60

So,

P(A/B)=P(A⋂B)/P(B)=8/26=4/13

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The two numbers are 7/6 and 5 when the sum of two numbers is 3 more than four times the first number.

Let's call the two numbers x and y, where x is the first number and y is the second number.

The problem gives us two equations that relate the two numbers:

[tex]x + y = 3 + 4x\\y - x = 2y - 10[/tex]

We can substitute the expression for y from equation 1 into equation 2:

[tex]y - x = 2(3 + 4x) - 10[/tex]

Expanding the right side and simplifying, we get:

[tex]y - x = 6 + 8x - 10\\y - x = 8x - 4[/tex]

Adding x to both sides:

[tex]y = 9x - 4[/tex]

Substituting this expression for y into equation 1:

[tex]x + (9x - 4) = 3 + 4x[/tex]

Expanding and simplifying the right side:

[tex]10x - 4 = 3 + 4x[/tex]

Subtracting 4x from both sides:

[tex]6x - 4 = 3[/tex]

Adding 4 to both sides:

[tex]6x = 7[/tex]

Dividing both sides by 6:

[tex]x = 7/6[/tex]

Substituting this value of x back into the expression for y:

[tex]y = 9x - 4 = 9 * (7/6) - 4 = 63/6 - 4 = 9 - 4 = 5[/tex]

So the two numbers are 7/6 and 5.

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Based on the table, the number of widgets that the company should produce will be B. 4

Gain is the best definition of profit, particularly when it is attained by raising the price of goods so that consumer spending exceeds producer expenses and a sizable return on investment is left. Profit is the amount of money that remains after expenditures and expenses have been paid.

This table shows how much it costs for a company to produce x number of widgets, and how much revenue the company makes for each additional widget produced. The widget should be based on where the most profit will be made. This is at 4 unit as the profit will be:

= $49 - $16

= $33

This is the highest profit that can be gotten.

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Answer:

The total average decrease in the stock after 8 weeks is -10 - 8 = -2 dollars.

Step-by-step explanation:

There are 45 possible choices for the five members.

There are ten people on the debate team, but only two of them can be in position 5. Positions 1 through 4 can be filled by any 10 members. Using the combination formula nCr, where n is the total number of items and r is the number of items chosen from that set, we can determine the number of ways to select these five members.

In this instance, we have 10C2, which simplifies to 10!/(2!(10-2)!)) or 10 items chosen from a set of 10. This can be reduced to 45, or 109/2. As a result, there are 45 ways to select the five debate team members.

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The length of the stone walkway would be 536.64 inches.

To find the length of the stone walkway, the landscaper needs to determine the length of the diagonal of the rectangular lawn.

The length of the diagonal can be calculated using the Pythagorean theorem:

[tex]d^2 = l^2 + w^2[/tex]

Where d is the length of the diagonal, l is the length of the rectangle, and w is the width of the rectangle.

So to find the length of the walkway, the landscaper would need to know the length and width of the rectangular lawn.

Suppose a landscaper wants to place a stone walkway from one corner of a rectangular lawn that is 40 feet long and 20 feet wide to the opposite corner.

Using the Pythagorean theorem, we can calculate the length of the diagonal:

[tex]d^2 = 40^2 + 20^2[/tex]

[tex]d^2 = 1600 + 400[/tex]

[tex]d^2 = 2000[/tex]

[tex]d =\sqrt{2000}[/tex]

[tex]d = 44.72 feet[/tex]

Rounding to the nearest inch, the length of the stone walkway would be 44.72 * 12 = 536.64 inches, which can be rounded to 536 inches.

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The equation for the Bowler world is c = $1.1g + $5,

The equation for the Lucky spares is c = $1.5g + $3.

and the cost is the same for 5 games and the cost is $10.5.

Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.

Both linear equations with one variable and those with two variables exist.

Given the Bowler, World charges $5.00 to rent shoes and $1.10 per game. Lucky Spares charges $3.00 for shoes and $1.50 per game.

Part A

using g for the number of games and c for the cost

for Bowler World

charges for shoes = $5

cost for per game = $1.1

cost for g games = $1.1g

total cost c =  $1.1g + $5 ..........(1)

for Lucky spares

charges for shoes = $3

cost for per game = $1.5

cost for g games = $1.5g

total cost c =  $1.5g + $3 ..........(2)

B. if the cost used in both places is equal then equation 1 equals equation 2

so $1.1g + $5 = $1.5g + $3

1.5g - 1.1g = 5 - 3

0.4g = 2

g = 2/0.4

g = 5

and cost is c =  $1.1g + $5

c = 1.1*5  + 5

c = 5.5 + 5

c = $10.5

Hence equations are  c =  $1.1g + $5 and  c =  $1.5g + $3,

and the cost is same for 5 games and the cost is $10.5.

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Answer:

2a+4+b+d

Step-by-step explanation:

a+a= 2a

4+0=4

b+0=b

c+0=c

d+0=c

The equation solved for the variable y is:

y = 4 - x

To do this, we need to isolate the variable y in the given equation.

We have the equation:

3y -2 = 10 - 3x

Adding 2 in both sides we will get:

3y -2 +2 = 10 - 3x + 2

3y = 12 - 3x

Now we can divide both sides by 3 to get:

3y/3 = (12 - 3x)/3

y = 4 - x

That is the equation solved for y.

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Answer:

Below

Step-by-step explanation:

The ENTIRE perimeter of a circle is  pi * d

 a semi circle circumference is 1/2 of this  1/2 pi * d   PLUS the diameter line

               1/2 pi * ( 2 mm)  + 2mm = 5.14 mm

There were 27 commercials during the shows. The unit rate of commercials per hour must be determined. As a result, the hourly unit rate is 18 commercials. And it is determined by Division.

A division is the process of dividing a given amount into equal parts.

Wendy spent one and a half hours on Saturday morning watching her favourite shows on television.

There were 27 commercials during the shows.

The unit rate of commercials per hour must be determined.

To find this we have to devide 27 by number of hours I.ei.e [tex]\frac{27}{1\frac{1}{2} }[/tex]

Convert [tex]1\frac{1}{2}[/tex] to improper fraction= [tex]\frac{27}{\frac{3}{2} }[/tex].

When a whole number is devided by fraction, the denominator is multiplied with the whole number= [tex]27*\frac{2}{3} =\frac{54}{3} =18.[/tex]

Hence, the unit rate is 18 commercials per hour.

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The value of 'x' in the expression (1/2)(4x - 5) + 5/2 = 10 is, x = 5.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, An expression  (1/2)(4x - 5) + 5/2 = 10.

(1/2)(4x - 5) = 10 - 5/2.

(1/2)(4x - 5) = (20 - 5)/2.

(1/2)(4x - 5) = 15/2. ('2' on both sides of the denominator cancels)

4x - 5 = 15.

4x = 20.

x = 5.

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If x and y are complementary angles, then x and y are supplementary vertical.

Complementary angles are two angles whose sum is equal to 90 degrees. Supplementary vertical angles are two angles that are vertically opposite each other and add up to 180 degrees.

Therefore, the correct answer is as given above. It could then be concluded that the correct answer in the case of x and y being complementary angles, then x and y are supplementary vertical.

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Answer:

3%=0.03 3%1÷2 =0.015. ..........,...

[tex]3 \frac{1}{4} - 4 \frac{1}{2} \\ \\ \longrightarrow \: \frac{13}{4} - \frac{9}{2} \\ \\ taking \: LCM \\ \\ \longrightarrow \: \frac{13 - 18}{4} \\ \\ \longrightarrow \: \boxed{ \frac{ - 5}{4} }[/tex]

hope helpful! :-;

[tex]10~~ : ~~45\implies \cfrac{10}{45}\implies \cfrac{5\cdot 2}{5\cdot 9}\implies \cfrac{5}{5}\cdot \cfrac{2}{9}\implies \cfrac{2}{9}\implies 2~~ : ~~9[/tex]

Answer:

-12

Step-by-step explanation:

Answer: -12

Step-by-step Explanation: 2 times -3= -6, -6 times 2= -12

Answer:

you count from the top to the bottem

Step-by-step explanation:

So it's...

[tex] \frac{5\pi}{4} - \frac{\pi}{4} [/tex]

Since the denominators are the same (both of the fractions have 4 on the bottom), you can do simple subtraction to the top while keeping the bottom 4

[tex]5\pi - \pi = 4\pi[/tex]

Which means the answer is

[tex] \frac{4\pi}{4} [/tex]

[tex]~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] ~\dotfill\\\\ \left( \cfrac{1}{3^2} \right)^{-1}\implies \left( \cfrac{3^2}{1} \right)^{+1}\implies 3^2\implies 9[/tex]

We will need 14 lb of raisins for a mixture worth of $2.75/lb

They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.

According to the data problem,

Lets call (x) = number of pounds of raisins we have:

$3.00(x)+$2.40(10) = $2.75(10+x)

3x + 24 = 27.5 + 2.75x

3x - 2.75x = 27.5 - 24

Clearing the variable we have:

0.25x = 3.5

x = 3.5/0.25

x = 14

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Answer:

(5 , -6) I believe this is the answer because I tried it

Tthe population of the colony after 2 hours is 64a

From the question, we have the following parameters that can be used in our computation:

Rate = doubles every 20 minutes

Represent the initial population with a

So, we have the following representation

f(t) = a(2)^t

Where t is the number of 20 minutes in the time

The time is given as 2 hours

So, we have

t = 2 hours/20 minutes

Evaluate

t = 6

The function becomes

f(t) = a(2)^6

Evaluate

f(t) = 64a

hence, the population is 64a

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The cubic expression of (1 + i) is given as follows:

(1 + i)³ = 0.

The cubic expression is obtained elevating the binomial (1 + i) to the third power, as follows:

(1 + i)³.

Then we expand the expression, applying the rule for the cube of a binomial, hence:

(1 + i)³ = i³ + i² + i + 1.

The basic complex number relation is:

i² = -1.

Hence:

i³ = i² x i = -1 x i = -1.

Then the expression is given as follows:

i³ + i² + i + 1 = -i - 1 + i + 1 = 0.

The problem asks for the cubic expression for (1 + i).

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Answer:

x= 10.2 when rounded to nearest tenth

The constant of variation is 62.5 and this means that the bus travel 62.5 miles per hour.

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

We have to given that;

The given relation is,

⇒ y = 62.5x

Where, y represent distance in mile and x represent the time in hour.

We know that;

The proportional relation is defined as;

⇒ y = kx

Where, k is constant of variation.

Hence, By comparing,

The constant of variation is 62.5 and this means that the bus travel 62.5 miles per hour.

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Answer: The Y intercept is 50 and it represents where the temperature starts.

Step-by-step explanation: The Y intercept is basically where the line is touching on the y line.

Answer:

93

Step-by-step explanation:

triangle = 1/2*5*6=15

B = 9*6=54

C = 4*6=24

total =54+24+15 = 93

Answer:

Step-by-step explanation:

the rise is 100