In the 30-60-90 triangle below, side s has a length of________ and side q has a length of_______
A. 16√3, 5
B. 8-5, 16
C. 4, 8√3
D. 4√2, 4√2
E. 4, 4.5
F. 16√3, 16√3

The given two triangles are similar to each other by the postulate called SAS.

What is triangle ?

Triangle can be defined as in which it consists of three sides, three angles and sum of the three angles are 180 degrees always.

Given,

The triangles are RST and UVT

So

From the given figure we can say that,

RT = TU

RS = VU

As two sides are already equal and vertically opposite angles are always equal .

so we can say that By postulates SAS we can say that they are similar to each other.

Hence, The given two triangles are similar to each other by the postulate called SAS.

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You should order 197.5 hats and 12.5 pairs of sunglasses to lose the least amount of money in the sales promotion.

This is a linear programming problem, which can be solved using a system of equations.

Let x be the number of hats sold and y be the number of pairs of sunglasses sold.

From the problem, we know the following constraints:

x >= 2y (since for every pair of sunglasses sold, two hats must be sold)

x + y >= 210 (to ensure that the items fill out the display)

y <= 100 (the maximum number of pairs of sunglasses that can be ordered)

We also know that the profit per hat sold is -$3 and the profit per pair of sunglasses sold is -$2.

So, the objective function is:

-3x - 2y (to minimize the loss)

Now we can use the equations and inequalities to find the optimal solution.

x >= 2y

x >= 4y

y <= 100

x + y >= 210

x >= 8y

y <= 100

x + y >= 210

Now we can use the equation to find the optimal solution

x = 8y

y <= 100

x + y >= 210

8y <=100

y <= 12.5

x + y >= 210

x >= 210 - y

Now we can find the value of x, y

y = 12.5

x = 210 - y

x = 210 - 12.5

x = 197.5

So the optimal solution is to order 197.5 hats and 12.5 pairs of sunglasses.

You should order 197.5 hats and 12.5 pairs of sunglasses to lose the least amount of money in the sales promotion.

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A linear combination of the values of a1 = (1,-2,0), a2 = (0,1,2), and a3 = (5,-6,8) with the corresponding weights is b = (2,-1,6).

We may construct a system of equations using the coefficients of the linear combination and the elements a1, a2, and a3 to determine whether b is a linear combination of a1, a2, and a3.

It is possible to write the equation for a linear combination of the type b = k1a1 + k2a2 + k3a3 in the following way:

b = k1 × (1,-2,0) + k2 × (0,1,2) + k3 × (5,-6,8) (5,-6,8)

So,

x = k1 + 5k3

y = -2k1 + k2 - 6k3

z = 2k2 + 8k3

From b =, we know the values of x, y, and z. (2,-1,6)

Thus, we can construct the equations in the following system:

x = k1 + 5k3 = 2

y = -2k1 + k2 - 6k3 = -1

z = 2k2 + 8k3 = 6

To determine the values of k1, k2, and k3, we can solve the system of equations using techniques like substitution or elimination.

k1 = 1, k2 = 3, k3 = 1

As a result, we can write b as a linear combination of the variables a1, a2, and a3 with the respective weights of (1, 3, and 1) for k1, k2, and k3.

b = 1a1 + 3a2 + 1 × a3

This indicates that b is a linear combination of the three variables a1, a2, and a3 with the weights (1, 1, and 3, respectively).

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Answer:

D. {x | x > 2}

Step-by-step explanation:

Separately solve inequalities:

[tex]\displaystyle{3x-2 > -11 \ \: \text{and} \ \: -2x+1 < -3}[/tex]

For left inequality, add 2 both sides. For right inequality, subtract 1 both sides:

[tex]\displaystyle{3x-2 +2 > -11+2 \ \: \text{and} \ \: -2x+1-1 < -3-1}\\\\\displaystyle{3x > -9 \ \: \text{and} \ \: -2x < -4}[/tex]

For left inequality, divide both sides by 3. For right inequality, divide both sides by -2 and also switch from < to > since the coefficient of x is negative:

[tex]\displaystyle{\dfrac{3x}{3} > \dfrac{-9}{3} \ \: \text{and} \ \: \dfrac{-2x}{-2} > \dfrac{-4}{-2}}\\\\\displaystyle{x > -3 \ \: \text{and} \ \: x > 2}[/tex]

Since both are in form of x > a and x > b, consider for highest value (since putting value below than 2 would make the other inequality false but if we put value higher than 2 then it'd make both inequalities true) which is x > 2.

Answer: Kayak Central

Step-by-step explanation:

Surf Bargains is 31.54 for 2 hours, if you want to find the hourly cost your going to do 31.54/2= 15.76 So Surf Bargains is 15.76 per hour.

Kayak Central you will do the same thing, 43.96/3.5= 12.56 per hour.

This means kayak central offers the lowest rate of $12.56 per hour.

We can see that height is the dependent variable and age is independent.

Therefore the graph of the relation, if connected, is a line segment parallel to the x-axis.

If we prove it with the vertical line test it will pass the test. Hence we can state it is a function.

The domain is:

The range is:

Answer: 22 minutes

Step-by-step explanation: m + 2m + m + 7 = 4m + 7

4m + 7 = 50

4m = 44

m = 11

2m = 11 x 2 = 22 minutes

Answer:

Step-by-step explanation:

I think anyone needs to care about the school bus, it's just a bus, and maybe the people inside are like you, so relax, keep calm on a school bus

Answer:

Step-by-step explanation:40

41

+

9

i

41

The  percentage of community service Joe still need to complete is 45%,

the correct option is C

Suppose the value of which a thing is expressed in percentage is "a'

Suppose the percent that considered thing is of "a" is b%

Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).

We need to Write the percent as a fraction in simplest form

16.24%

So, we can rewrite it as;

16.24 / 100

16 and 24/100 or 16 6/25

So the percent as a fraction is 16 6/25.

Given;

Total number of hours joe has to perform= 40

Number of hours joe has already performed= 18

Now;

Percentage;

=18*100/40

=18*5/2

=45

Therefore, the percentage will be 45%

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The equation of the plane is:-6x + 0y + 6z - 18 = 0

The equation of a plane containing a point P(x1, y1, z1) and a line defined by x = x0 + at, y = y0 + bt, z = z0 + ct, is given by:

Ax + By + Cz + D = 0

Where:

A = (y1 - y0)a - (x1 - x0)b

B = (z1 - z0)a - (x1 - x0)c

C = (z1 - z0)b - (y1 - y0)c

D = -(A*x1 + B*y1 + C*z1)

Plugging in the given values, we have:

A = (1 - 5)3 - (1 - 3)5 = -6

B = (3 - 1)3 - (1 - 3)2 = 0

C = (3 - 1)5 - (1 - 5)2 = 6

D = -(-6*1 + 0*1 + 6*3) = -18

Therefore, the equation of the plane is:

-6x + 0y + 6z - 18 = 0

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The scale will register a weight greater than 80 pounds due to Newton’s Third Law

Given that there is a 1-liter container filled with 500 milliliters of water placed on top of a scale displaying 80 pounds.will register a weight greater than 80 pounds

When a body is submerged in a water an upward force acts on the body known as buoyant force which is equal to weight of the water displaced by the body. Since water exerts Buoyant force on the body and according to Newton's third law there must be equal and opposite force exerted by the body on the water. This additional force equal and opposite to the Buoyant force will cause the reading of the scale to increase. Therefore the scale will register a weight greater than 80 pounds due to Newton’s Third Law.

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The complete question is :

There is a 1-liter container filled with 500 milliliters of water placed on top of a scale displaying 80 pounds. When a metal cube is submerged tied to a string end into the container, which of the following statements accurately describes the result?

The cube’s density must be provided to predict what will happen

The scale will remain at 80 pounds until the cube is floating on top of the water fully submerged.

The scale will register a weight greater than 80 pounds due to Newton’s Third Law

The scale will register a weight greater than 80 pounds due to Newton’s Third Law

The interval of time that has the average rate of change being the smallest is 1. 2002 - 2004.

From the information given, the table shows the year and the number of households in a building that had high-speed broadband internet access.

In this case, the average rate of change from 2002-2004 will be:

= 23 - 11

= 12

The average rate of change from 2004-2006 will be:

= 47 - 23

= 24

The average rate of change from 2003-2005 will be:

= 33 - 16

= 17

The smallest is from 2002 to 2004.

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The artist needs 78,835.2 cm² of metal to make the sculpture.

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The total cost function C is  T(x) =  0.000001x³ - 0.03x² + 200x + 15,000, the total profit function P is P(x) = 0.000001x³ - 0.01x² + 50x + 15,000 and the profit for the company if 1,900 units are produced and sold each week is $80,759

The term function in math is  written as  a rule that gives value of a dependent variable that corresponds to specified values of one or more independent variables.

Here we have given that the division of Chapman Corporation manufactures a pager.

Here we also know that the weekly fixed cost for the division is $15,000, and the variable cost for producing x pagers/week in dollars is represented by the function V(x).

Then the function is written as,

=> V(x)= 0.000001x³ - 0.01x² + 50x.

Here we have given that company realizes a revenue in dollars from the sale of x pagers/week represented by the function R(x).

Then the function is written as,

=> R(x)= -0.02x² + 150x Where the value of x lies between (0<x<7500)

Then the total cost is calculated as,

=> T(x) = Total Cost + fixed cost + variable cost

Then apply the values on it, then we get,

=> T(x) = 15,000 + 0.000001x³ - 0.01x² + 50x - 0.02x² + 150x

=> T(x) =  0.000001x³ - 0.03x² + 200x + 15,000

And the total profit function is written as,

=> P(x) = 0.000001x³ - 0.03x² + 200x + 15,000 - (-0.02x² + 150x)

=> P(x) = 0.000001x³ - 0.01x² + 50x + 15,000

If the is the profit for the company if 1,900 units are produced and sold each week, then the profit is calculated as,

=> P(1900) = 0.000001(1900)³ - 0.01(1900)² + 50(1900) + 15,000

=> P(1900) = 80759

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Taking k as a common factor on the first expression, we can rewrite that into the second one, thus, the expressions are equivalent.

Two expressions are equivalent only of we can, using algebra, rewrite one of the expressions into the other one.

The two given expressions are:

k + 0.10k

and

1.1k

Now let's take the first expression:

k + 0.10k

We can take k as a common factor, then we will get:

k + 0.10k = (1 + 0.10)k = 1.1k

So yea, the two expressions are equivalent.

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The bearing of B from S = 63.8 + 180 = 243.8°

To calculate the distance that the boys walked, you would need to know their speed and the duration of their walk.

Speed is typically measured in units such as miles per hour (mph) or kilometers per hour (kph). If you know the speed of the boys and the duration of their walk in hours, you can calculate the distance they walked using the formula: distance = speed x time.

To calculate the bearing of S from B, you can use the following steps:

Calculate the distance between S and B using the Pythagorean theorem. The distance is the hypotenuse of a right triangle, where one side is 8.6 km (the north-south distance) and the other side is 12.5 km (the east-west distance).

Calculate the angle formed by the distance between S and B and the north-south line. To do this, you can use the arctangent function (atan), which returns the angle in radians.

To convert radians to degrees, multiply by 180/π

The bearing of S from B = atan(12.5/8.6) x 180/π = 63.8°

To calculate the bearing of B from S, you just need to add 180 degrees to the bearing of S from B

The bearing of B from S = 63.8 + 180 = 243.8°

b. 243.8

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Complete question:

A bank B is 8.6 km north and 12.5 km west of a school S.

Calculate correct to 3 significant figures:

a the bearing of S from B

b the bearing of B from S.

On a variable ratio schedule, reinforcement is given for the next correct response after varying numbers of responses have been made.

What is variable ?

A variable is a value or quantity that can change or take on different values in a given context or system. In mathematics and science, variables are often used to represent unknown or changing values in an equation or model. In programming, a variable is a named container or storage location that holds a value that can be modified during the execution of a program.

On a variable ratio schedule, reinforcement is given for the group of correct responses that occur after varying amounts of time have passed. This means that the reinforcement is not given after a fixed number of responses or after a fixed amount of time has passed. Instead, the reinforcement is given after a varying number of correct responses have been made, making it unpredictable for the individual or organism being reinforced. This type of schedule is often used in gambling and other situations where the reinforcement is desired to be unpredictable and maintain the individual's interest or motivation.

On a variable ratio schedule, reinforcement is given for the next correct response after varying numbers of responses have been made.

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In a case whereby Dominic is making and  uses 3/4 cup of breadcrumbs for every 11/4 pounds of ground beef the number of  cups of breadcrumbs he need when he uses 1 pound of ground beef is 3/5.

The concept that will be used here is fraction. fraction: A number that is stated as a quotient in mathematics, when the numerator and denominator are divided. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

Since Dominic is using 3/4 cup of breadcrumbs for every 11/4 pounds of ground beef

The amount that will be needed for  1 pound of ground beef will now be:

11/4 pounds =  3/4 cup

we can convert to improper fraction as

5/4 * 3/4

12/ 20= 3/5

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complete question:

Dominic is making meatballs. He uses 3/4 cup of breadcrumbs for

every 11/4 pounds of ground beef. How many cups of breadcrumbs

does he need when he uses 1 pound of ground beef? *

It will take them 28 minutes to fill the tank.

The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.

Given:

The first pipe alone can fill the tank in 84 minutes.

So, the rate at which the first pipe fills the tank = 1/84

and, The second pipe can fill the tank in 42 minutes by itself.

So, the rate at which the second pipe fills the tank =1/42

If they work together, they would work simultaneously and their individual rates are additive.

= 1/84 + 1/42

let it takes t hours for both pipes to fill the tank working together, the working rate per minute would be 1/t. Therefore,

1/84 + 1/42 = 1/t

3/84 = 1/t

t = 84/3

t = 28 minutes

Hence, 28 minutes will take to fill.

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Answer:

32%

Step-by-step explanation:

1552 / 4850 = 0.32

The probability that you select a gold marble is, 1/21.

The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

We have to given that;

A bag contains 2 gold marbles, 10 silver marbles, and 30 black marbles.

Here, Number of gold marbles = 2

And, Number of total marbles = 2 + 10 + 30

                                              = 42

Hence, The probability that you select a gold marble is,

⇒ Number of gold marbles / Total number of marbles

⇒ 2 / 42

⇒ 1 / 21

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The cost per ounce of a container of gochujang at the market can be calculated using the equation of the line of best fit.

The line of best fit is given by the equation y = 0.14x + 1.3, where y is the cost of the container and x is the amount of sauce in the container (in ounces). To calculate the approximate cost per ounce of a container of gochujang, we can use this equation. We set y = 1, since we want the cost of one ounce of sauce. The equation of this line is y = 0.25x + 3.2, where x is the amount of sauce in the container and y is the cost of the container. To find the cost per ounce, we need to divide the y-intercept, 3.2, by the slope, 0.25. This gives us 12.8. Therefore, the approximate cost per ounce of a container of gochujang at the market is $12.8.

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A 1.5 standard deviations above the mean IQ score is 122.5.

An expression that depicts the relationship between two or more numbers and variables is called an equation.

A dependent variable is one that depends on another variable, whereas an independent variable does not depend on any other variable for its value.

Giving the z score are:

z is calculated as (raw score - mean) / standard deviation.

with a standard deviation of 15 and a mean of 100. The z-score of 1.5 is equal to the IQ score that is 1.5 standard deviations above the mean, so:

1.5 = (x - 100)/15

x = 122.5

A 1.5 standard deviations above the mean IQ score is 122.5.

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The amount of time that it took for Abby to meet Betty is given as follows:

2 minutes.

The quadratic function giving Abby's distance from home is defined as follows:

s(t) = -100t² + 400t.

The coefficients of the function are given as follows:

a = -100, b = 400.

The vertex of the quadratic function is the turning point of the graph, that is, the moment that Abby meet Betty.

The t-coordinate of the vertex is given as follows:

t = -b/2a

t = -400/-200

t = 2 minutes.

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the star of the mentioned, figure is attached below.

What is a star?

A polygon, which is a form with many sides, is a type of star. In fact, five-pointed stars are categorised as decagons or polygons with ten sides, although the number of sides changes depending on the number of points on the star, such as six, ten, etc. An equilateral and equiangular polygon that self-intersects is referred to as a regular star shape or regular star polygon. It was made by connecting the vertices of a straightforward, regular, n-sided polygon to one another in a nonadjacent direction until the original vertices were once again reached.

How are stars with five points made?

All stars are formed by lines at particular angles. The basic pattern is as follows in the case of five-pointed stars, which are the most prevalent:

Use lines of the same length and rotate 135° each time.

Hence the star of the mentioned figure is attached below.

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The force the road exerts on the car as the car passes the highest point of the bump n=mg−mv²/R

Newton's second law of motion defines the behavior of objects for which all existing forces are not balanced.

The second law states that the acceleration of an object is dependent upon two variables - the net force acting upon the object and the mass of the object.

The acceleration of an object depends directly upon the net force acting upon the object, and inversely upon the mass of the object.

The free-body diagram given below shows the forces on the car in the vertical direction. Newton’s second law then gives

∑F y=may = mv²/R

mg−n=mv²/R

n=mg−mv²/R

When n=0, mg=mv²/R​

Then, v= √gR

A more gently curved bump, with a larger radius, allows the car to have a higher speed without leaving the road. This speed is proportional to the square root of the radius.

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True, The Laffer curve shows the exclusively direct relationship that exists between tax rates and tax revenues

The Laffer Curve was developed by Arthur Laffer. Arthur, a supply side economist used this curve to show the relationship that existed between tax rates and also the amount of tax revenue which the government takes or collects. This curve provides an illustration to his argument that sometimes when tax rates are cut there could be increase in total tax revenue.

True, The Laffer curve shows the exclusively direct relationship that exists between tax rates and tax revenues

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