B and C are sets of real numbers defined as follows.

Write B U C and B C using interval notation.
If the set is empty, write .
B= {x|x>3}

C= {x|x≤5}

The horizontal distance that the jet has traveled in 10 seconds will be 3000feet and the jet’s altitude at this time is 6.44 minutes

Given: A plane flies off at a 15-degree angle and 350 feet per second.

Find The time needed to ascend to a height of 35,000 feet.

Imagine a right triangle with a 15-degree angle at the origin at Q1.

The plane's flight route is the hypotenuse.

speed = distance/time

speed * time = distance

distance = 300*10 = 3000feet

Sin(15) = opposite / hypotenuse

Sin(15) = 35000 / (350*t)

350*t  =  35000 / Sin(15)

t  =  35000 / (350 * Sin(15)

t  =  100 / Sin(15)

t   = 100 / .25882

t   =  386.37 seconds

t = (386.37 sec) * (1 min. / 60 sec)  = 6.44 minutes

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Answer:

48×14 in.

Step-by-step explanation:

[tex]50^{2} =48^{2} +14^{2}[/tex]

[tex]2500=2304+196[/tex]

[tex]2500=2500[/tex]

The TV screen is 48 inches long and 14 inches high.

Hope this helps.

the value of functions f(-2)=-15, g(3) =12.

What is a function?

A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.

The x-values are input into the function machine. The function machine then performs its operations and outputs the y-values. The function within can be any function.

f(x) = 4x - 7

g(x) = 4*x

f(-2) = 4(-2)-7 = -8-7 = 15

g(3) = 4*3 = 12

Hence the value of functions f(-2)=-15, g(3) =12.

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Complete the pyramid with the corresponding values

Since each number is the product of the two numbers directly below it. Then the pyramid can be completed as follows:

Check the attached image for labeling.

j = -1 × -1 = 1

h = -2 × j = -2 × 1 = -2

y = h × -1 = -2 × -1 = 2

j × n = -1

1 × n = -1

n = -1

n × m = 2

-1 × m = 2

m = -2

w = -1 × 2 = -2

t = y × w = 2 × -2 = -4

-1 × k = n

-1 × k = -1

k = 1

k × l = m

1 × l = -2

l = -2

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With the help of algebraic expression, there were 8 small tables and 4 large tables in the local cafe.

Algebraic expressions serve as the mathematical statement when operations such as addition, subtraction, multiplication, division, etc. are performed on variables and constants. Let's imagine that while playing with matchsticks, James and Natalie came up with the idea to arrange the sticks into patterns that represented numbers.

James drew a four in the air with four matchsticks. Natalie was able to make a pattern with two 4s by putting three more matchsticks on the board. They realised they could proceed to add three matchsticks each round until they had a total of four. This led them to the conclusion that, in general, 4+ 3(n-1) sticks are needed to make a pattern with n numbers of 4s. This sentence makes reference to the algebraic expression 4+ 3(n-1).

The total no. of tables are 32

Let x be the no. of Small tables = 2x

And y be the no. of Large tables = 4y

Total no. of tables = 12

2x + 4y = 32

And

x + y = 12

x = 12 - y

Putting the value of x in first equation

2(12 - y) + 4y = 32

24 - 2y + 4y = 32

4y - 2y = 32 - 24

2y = 8

y = 4

And Putting the value of y in 2nd equation

x = 12 - (4)

x = 8

Thus, With the help of algebraic expression, there were 8 small tables and 4 large tables in the local cafe.

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Answer:

Step-by-step explanation:

ham 3.45x

Using division we know that each person will have 1/4 pound of Skittles.

In mathematics, the division is the process of dividing a number into equal parts and calculating the maximum number of equal parts that may be formed.

For instance, dividing 15 by 3 results in the division of 15 into 3 groups of 5 each.

The division sign, "," or occasionally "/," is used in computer code.

So, we know that:

Lauren and Shayla have 1/2 pound of Skittles

They will share it with 2 more people.

Then, each will have:

(1/2)/2

1/2 / 2

1/2 * 1/2

1/4

Therefore, using division we know that each person will have 1/4 pound of Skittles.

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Answer: A: what would be population equal 100 years from now?

Step-by-step explanation: I hope this helps!

Check the picture below.

[tex]\textit{Law of sines} \\\\ \cfrac{sin(\measuredangle A)}{a}=\cfrac{sin(\measuredangle B)}{b}=\cfrac{sin(\measuredangle C)}{c} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{\sin(18^o)}{1.9}=\cfrac{\sin(59^o)}{j}\implies j=\cfrac{1.9\sin(59^o)}{\sin(18^o)}\implies j\approx 5.3~in[/tex]

Make sure your calculator is in Degree mode.

The length of side J is 5.6 inches.

A triangle is a 2-D figure with three sides and three angles.

The sum of the angles is 180 degrees.

We can have an obtuse triangle, an acute triangle, or a right triangle.

We have,

To find the length of side J, we can use the law of sines, which states that for any triangle with sides a, b, and c opposite to angles A, B, and C respectively:

a/sin(A) = b/sin(B) = c/sin(C)

In this case, we know that side K is 1.9 inches, and angles J and K are 59° and 18° respectively.

Let's use the law of sines to find the length of side J:

J/sin(59°) = 1.9/sin(18°)

J = (sin(59°)/sin(18°)) * 1.9

J ≈ 5.6 inches

(rounded to the nearest tenth of an inch)

Therefore,

The length of side J is approximately 5.6 inches.

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Answer:

yes

Step-by-step explanation:

they are perpendicular so you can use 52/2 =26

26² + 33² = LM²

She should use the equation k = P/x². The correct answer would be an option (D).

The term "equation" refers to mathematical statements that have at least two terms with variables or integers that are equal.

The potential energy, P, in spring is represented using the formula, as follows:

P = kx²

Solve for variable k and we get the equation:

k = P/x²

When we compare this equation to the provided possibilities, we can easily see that it corresponds to the last option.

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Answer:

  D)  500(1 +.03/4)^(4(5))

Step-by-step explanation:

You want to know the expression you would input to a calculator to find the money Joe will have in his account from a $500 deposit earning 3% interest compounded quarterly for 5 years.

The value of the account is given by the formula ...

  A = P(1 +r/n)^(n·t)

where P is the principal invested, r is the annual rate, n is the number of times per year interest is compounded, and t is the number of years.

Filling in the given values, you would want your calculator to evaluate ...

  500(1 +.03/4)^(4(5)) . . . . . . . matches choice D

__

Additional comment

The attachment shows a couple of different calculator inputs that could be used to find the account value. Note that the product (4)(5) is the exponent of the base (1 +.03/4). This calculator uses the caret (^) key to open the exponent expression.

The calculator also has a "future value" function that will compute the same result.

The value in the account will be $580.59.

<95141404393>

The two rational numbers that result in the lowest product are given as follows:

18.5 and -12.4.

For the product of two rational numbers, we have that their signal is given as follows:

For the lowest product, we want a negative number, with the highest absolute value, hence we take the lowest negative and highest positive, as follows:

18.5 and -12.4.

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The average of three consecutive numbers 17, 18, 19 is 18 and the average of three consecutive numbers -100, -99, -98 is -99

Consider the three consecutive numbers 17, 18, 19.

We find the average number would be found by adding all the terms and dividing by 3:

(17 + 18 + 19)/3

= (54)/3

= 18

consider another example: three consecutive numbers are -100, -99, -98.

Their average would be,

[-100 + (-99) +  (-98) ] ÷ 3

= -297  ÷ 3

= -99

We can observe that the average of three consecutive numbers is the second term given in that set.

Let m, m + 1,  m + 2 be set of any three consecutive numbers.

The average of these three consecutive numbers would be,

A = [m + (m + 1) + (m + 2)] ÷ 3

A = (3m + 3) ÷ 3

A = 3(m + 1) ÷ 3

A = m + 1

Thus, the rule will always work, as we know that average is the central value of a set of numbers.

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The complete question is:

Consecutive numbers follow one right after the other. An example of three consecutive numbers is 17, 18, and 19. Another example is -100, -99, -98. Choose any set of three consecutive numbers. Find their average. What do you notice? Find the average of another set of three consecutive numbers. What do you notice? Explain why the thing you noticed must always work, or find a counterexample.​

The method used to assign probabilities when the results of experimentation or historical data are used to assign probability values is referred to as the relative frequency method.

The relative frequency method is a way to assign probability values to events based on how often they have occurred in the past.

The probability of an event is determined by counting the number of times the event has occurred in a given set of observations, and dividing that number by the total number of observations. For example, if a certain event has occurred 20 times out of 100 total observations, the probability of that event would be 0.2 (20/100). This method is based on the idea that the probability of an event is related to its frequency of occurrence in a large number of trials.

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Relative frequency distributions are generally more useful than frequency distributions when comparing data sets of the same size.

The frequency (or absolute frequency) of an event in statistics is the number of times the event occurred in an experiment or research. Histograms are frequently used to graphically show these frequencies.

The absolute frequency of an occurrence normalized by the total number of events is referred to as its relative frequency (or empirical probability). A frequency distribution can be created by plotting the values of all events.

A histogram is a graphical representation of tabulated frequencies that is displayed as consecutive rectangles erected at discrete intervals (bins) with an area equal to the frequency of the observations in the interval.

The frequency density of the interval, i.e. the frequency divided by the width of the interval, is also equal to the height of a rectangle.

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The area of a cross section perpendicular to one face is 16 square Inches and its perimeter is 16 inches.

The term perimeter in math is known as the total distance around the respective shape.

Here we know that the edge of a cube is 4 Inches.

Here we have to draw a sketch of a cube with side = 4 in as shown below..

Here we have to know that the shaded area is perpendicular to the right and left vertical faces of the cube, then the cross section is a square with each side equal to 4 in.

Hence the value of the area of the cross section is calculated as

=> 4*4 = 16 in²

And the value of the perimeter of the cross section is

=> 4+4+4+4 = 16 in.

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Answer:2.5cm

Step-by-step explanation:1cm =0.01 m

Alternative Hypothesis is sufficient evidence at the 0.05 level that the bags are underfilled.

In the given question, we have to explain that there is sufficient evidence at the 0.05 level that the bags are underfilled or not assuming that the population is normally distributed.

We can reject the null hypothesis if the sample contains sufficient data to refute the assertion that there is no effect in the population (p). Or else, we are not able to rule out the null hypothesis.

The claim in the alternative hypothesis that you anticipate or hope to be accurate.

The complement of the null hypothesis is the alternative hypothesis. The extensive nature of null and alternative hypotheses ensures that they account for all potential outcomes.

Since, bag filling machine works correctly at the 436 gram setting. Test the alternative hypothesis in place of the claim that the true mean is less than 436. This test has a left tail.

The null and alternative hypothesis are

H(0): μ = 436

H(a): μ < 436

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Answer:

8.4+3.5t

Step-by-step explanation:

8.4+3.5t

The area of a circle with a radius of 3.5cm rounded to the nearest tenth is 38.5 cm².

A circle is simply a closed 2-dimensional curved shape with no corners or edges.

The area of a circle is expressed mathematically as;

Area = πr²

Where r is radius and π is constant pi ( π = 3.14 )

From the diagram;

Plug the given value into the above equation and solve for A.

Area = πr²

Area = 3.14 × ( 3.5cm )²

Area = 3.14 × 12.25 cm²

Area = 38.5 cm²

Therefore, the area of the circle is 38.5 cm².

Option B) 38.5 cm² is the correct answer.

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30 different combinations can be made among six people.

The total number of arrangements is called Permutations.

According to the question,

There are 6 members to choose from.

And there are 2 posts to be filled. i.e, President, Vice-President.

Let's assume each position is a blank. Here each blank represents a placeholder.

The first position can be filled in 6 ways (because any one of the students can get that position)

The second position can be filled in 5 ways (as one person already got the first position, he can't get the second position).

The total number of ways all three positions can be filled in

= 6 * 5 = 30

So, the total number of ways in the combination = 30.

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Answer:

Hi, my name is Za'Riah! I will gladly help you with your problem. (see explanation)

Step-by-step explanation:

There really isn't much to explain or step out with this problem.

60% of 150 is 90

150 + 90 = 240 inches

The truck is 240 inches long.

Answer:

240

Using the similarity rectangle theorem, the value of FG is approx 23.

We determine the value of FG using the using the similar rectangle theorem.

Two rectangles must have proportional sides in order for them to be identical (form equal ratios). The two shorter sides should be proportionately equal to the two longer sides.

The rectangle ABCD and FGEH are both have same shape.

As we know that the rectangle same two sides equal. So

FG/EF = AD/DC

FG/15 = 18/12

Multiply by 15 on both side, we get

FG = 18/12 * 15

FG = 3/2 * 15

FG = 22.5

FG = 23 (approx)

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The complete question is:

Square 1 ABDC square 2 FGEH. AD= 18 DC=12 FE= 15. How do I find the square factor FG?

Answer:

Domain and Range. The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.

The domain of a function is the set of values that we are allowed to plug into our function. While a functions range, is the set of values that the function can take.

To be more precise, he domain of a function f(x) is the set of all values for which the function is defined, and the range of the function is the set of all values that f takes.

A relation's domain can also be discussed, where one element in the domain may be mapped to more than one element in the range.

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The slope is 1.33, the y-intercept is -1 and the equation is y = 1.333x -1.

The solution has been obtained using the slope intercept form.

What is slope intercept form?

The line with slope m and y-intercepts b is the graph of the linear equation y = mx + b. The values of m and c are real integers, and the form of the linear equation is known as the slope-intercept form.

A line's steepness is indicated by its slope, m. Sometimes, a line's slope is also referred to as its gradient. The y-coordinate of the place where the line's graph contacts the y-axis is represented by a line's y-intercept.

We are given graph with straight line.

The two points on the graph are (0,-1) and (3,3)

Let's find the slope(m)

[tex]m=\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

[tex]m=\frac{3+1 }{3 -0 }[/tex]

m = 4/3

m = 1.333

We know that b = y₁ - x₁(y₂ - y₁)/(x₂ - x₁)

So,

⇒b = (-1) - 0(3 + 1)/(3 - 0)

⇒b = -1 + 0

⇒b = -1

The equation comes out to be

⇒y = mx + b

⇒y = 1.333x -1

Hence, the slope is 1.33, the y-intercept is -1 and the equation is

y = 1.333x -1.

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Since, there are multiple questions, so the question answered above is attached below

17)

The situation models a function, the independent variable is the number of plans and the dependent variable is the cost.

b) The domain of the function is {x:x≤4} while the range is {y:y≤120}

18) The independent variable is the miles travelled and the dependent variable is the cost.

b) The domain of the function is  {x:x≤20} and the range is  {y:y≤72.8}

We know that the domain of the function represents all of the values can be assigned to the independent variable in the function while the range has to do with all the values that the functions can be able to return.

In this case, we have real life models and we are told to convert them into functions;

a) y = 30 x

b) y = 2.80 + 3.50x

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The set of ordered pairs represents a function would be; {(-4, 9), (-1,0), (0,9), (-4, 8), (0, 5)}.

Function is a type of relation, or rule, that maps one input to specific single output.

In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable). In mathematics and the physical sciences, functions are indispensable for formulating physical relationships.

We need to know that to be a function each x value (first component) has to have one only y value (second component).

In the option 1 the first component 1 has two different y values (-1 and 0),

In option 3 the x value 5 has two different y values (-5 and 9) and in option four the x value -3 has three different y values (1, 2 and -3).

Then, the correct option is the second one.

{(-4, 9), (-1,0), (0,9), (-4, 8), (0, 5)}.

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As per the statement the data are qualitative because they don't measure or count anything.

The term measurement in math is known as the process of associating numbers with physical quantities and phenomena.

Here we have the statement the types of food served by restaurants Italian, Chinese, fast, etc.

As we looking into the statement we have identified that the statement is defines the characteristics of the restaurant which is also defines that there is no value for counting in it.

So, this refers the quality of the product instead of quantity.

Which also defined that there is no measurement value in it.

Therefore, the correct option is (c).

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