Convert 284 °F to Celsius

Division problem with quotient of 3 and a remainder of 28 are-

The given data is-

To estimate:

division problem?

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The value of x in the problem is 0

Given that PQR is a straight line

In this problem PQ+QR=PR

The value of PQ is 9

The value of QR is not given but given an equation 2x+3

And QR is x+12

So PQ+QR=PR

9+2x+3=x+12

12+2x=x+12

2x-x=12-12

x=0

Therefore, the value of x in the problem is 0

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Answer:

864

Step-by-step explanation:

Answer:

≈20.35°

Step-by-step explanation:

height = 8

hypotenuse =23

angle is x

sin(x) =8/23

[tex]sin^{-1} (\frac{8}{23} )[/tex] ≈20.35°

x is about ≈20.35°

The ramp makes an angle of approximately 20.86 degrees with the ground.

Given that there is a truck with a ramp at a height of 8 feet the size of the ramp is 23 feet,

we need to find the angle ramp make with the ground.

To find the angle that the ramp makes with the ground, we can use the sine function.

The sine of an angle is equal to the opposite side divided by the hypotenuse in a right triangle.

In this case, the opposite side is the height of the ramp (8 feet), and the hypotenuse is the length of the inclined portion of the ramp (23 feet).

Let's calculate the angle:

sin(angle) = opposite/hypotenuse

sin(angle) = 8/23

To find the angle, we need to take the inverse sine (or arcsine) of both sides of the equation:

angle = arcsin(8/23)

We can find the approximate value of the angle:

angle ≈ 20.86 degrees

Therefore, the ramp makes an angle of approximately 20.86 degrees with the ground.

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As per the random sampling, the marginal relative frequency for action movies is 44%.

The term sampling refers the process of selecting the group that you will actually collect data from in your research.

Here we have given that  a relative frequency table that shows the percentage of comedy lovers that prefer each location and the percentage of drama lovers that prefer each location.

And we need to find the marginal relative frequency of action movies.

While we looking into the given question, we have identified that the joint relative frequency for 8th graders who like comedy movies is 16%. And the half of the 7th graders prefer action movies.

Based on these facts the resulting frequency is 44%.

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option D

Given;

larger cube edge length  -  3x+2 units

smaller cube edge length -  2x-1 units

We know that  volume of a cube  = (Edge of the cube)3

volume of larger cube = (3x+2 )³

                                     =27x³+8 +54x²+36x

volume of smaller cube=(2x-1)³

                                        =8x³-1 -12x²+6x

Volume difference = volume of larger cube -volume of smaller cube

volume difference =( 27x³+8+54x²+36x)-(8x³- 1 - 12x²+6x)

                                = 19x³+9+66x²+30x

                                 =19x³+66x²+30x+9

Hence volume of larger cube is greater by (19x³+66x²+30x+9)

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Answer: It's not possible for a positive, even integer to have a specific shape, such as the shape of a 4. This is because integers are abstract mathematical concepts that represent whole numbers and do not have any physical properties, such as shape. Additionally, even integers are simply integers that are divisible by 2, and do not have any specific shape associated with them.

If you're asking about a specific number that has the shape of a 4, such as the number "4" written in a specific way, it's important to note that the value of a number does not depend on its physical appearance. For example, the number 4 written as "4" and the number 4 written as "IV" (the Roman numeral for 4) are both the same number, and have the same value.

The expression [tex]\[\frac{4+6a}{5}-\frac{1+3a}{4}\][/tex] as a single fraction is [tex]\frac{9a-11}{20}[/tex]

What is algebraic expression ?

In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.). Terms comprise expressions.

According to question

⇒     [tex]\[\frac{4+6a}{5}-\frac{1+3a}{4}\][/tex]

⇒   taking LCM of 4, 5 = 20

now [tex]\[\frac{4(4+6a)-5(1+3a)}{20}[/tex]

⇒ (16 +24a - 5 - 15a)/20

⇒ ((24a - 15a) - (16-5))/20

⇒ (9a - 11)/20

hence, the expression  [tex]\[\frac{4+6a}{5}-\frac{1+3a}{4}\][/tex] as a single fraction is [tex]\frac{9a-11}{20}[/tex]

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The percent of increase Maria walked if found as the 50%.

The formula for the percentage increase is given as;

Percent increase = Increase / original number x 100

original number = 20 miles

Increase = 30 miles - 20 miles

Increase = 10 miles

So,

Percent increase = 10 / 20 x 100

Percent increase = 50%

Thus, the percent of increase Maria walked if found as the 50%.

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The correct question is-

9) Maria walked 20 miles yesterday. Today she walked 30 miles. What was the percent of increase Maria walked?

The composition of A and B represents by the set A o B = {(2,2),(4,0)}

What is a set of ordered pair?

An ordered pair in mathematics is a set of two things. The order of the objects in the pair matters because, unless a = b, the ordered pair differs from the ordered pair. Ordered pairs are also known as 2-tuples, or 2-length sequences.

Given sets are

A = {(1,2), (-3,0), (4,7)}

B = {(2,1), (0,3), (4,-3)}

The inputs of B are 2, 0, and 4.

The outputs of B are 1, 3, and -3.

The inputs of A are 1, -3, and 4.

The outputs of A are 2, 0, and 7.

The composition can be written as A o B = A(B(x)

A(B(2)) = A(1) = 2

A(B(0)) = A(3) = not valid [Since 3 is not an input of A].

A(B(4)) = A(-3) = 0

The composition is {(2,2), (4,0)}.

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Answer: [tex]14\sqrt 2[/tex]

Step-by-step explanation:

The angle of rotation is 90 degrees.

What is a square?

In a square, all the sides are equal in length and all the angles are right angles (90 degrees). The center of a square is the point that is equidistant from all four vertices, and it is also the point of intersection of the diagonals of the square.

The angle of rotation about the center that maps AB to BC is 90 degrees.

If we rotate the square about its center, the sides of the square will rotate to new positions. For example, if we rotate the square 90 degrees counterclockwise (as specified in the question), side AB will rotate to the position of side BC.

The angle of rotation that maps AB to BC is the angle through which the square was rotated.

Hence, the angle of rotation is 90 degrees.

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The balloon's vertical distance above the ground is 358.9 feet.

An angle is said to be that of depression when it is measured downwards with respect to the horizontal plane.

So that applying the appropriate trigonometric function to solve the question, we have;

Tan θ = Opposite side/ Adjacent side

But,

θ = 90 - 24

  = 66

θ = [tex]66^{o}[/tex]

Let the vertical distance of the balloon be represented by x.

Tan 66 = 806/ x

x = 806/ Tan 66

  = 806/ 2.246

  = 358.86

x = 358.9 feet

The balloon's vertical distance above the ground is 358.9 feet.

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Step-by-step explanation:

Hope u get it x=3×3

x=9

It didn't include in the photo

Answer:

Graph A

Step-by-step explanation:

Given piecewise function:

[tex]f(x)=\begin{cases}9+x, \;\;\:\:x\leq3\\x^2+3,\;\;x > 3\end{cases}[/tex]

To graph the given piecewise function:

The line  y = 9 + x  is a straight line with a positive gradient.  

It crosses the x-axis at (-9, 0) and crosses the y-axis at (0, 9).

Therefore, the only graph that shows the line  y = 9 + x  is the first graph.

Answer: $2,275.94

Step-by-step explanation: First, we need to find how much he pays for the stocks alone. So, we would use this equation:

41.09(55)

41.09 x 55

That would get us to $2,259.95. Now, we have to add the $15.99, bc he had to pay a fee. So $2,259.95 + 15.99 = $2,275.94. I hope this helped!

A bi-weekly visit to your favorite restaurant. Say on average you spend $25 each visit.

You will spend an average of $50 a week at this restaurant.

Answer:

-11

Step-by-step explanation:

4c - 3   Substitute -2 for c

4(-2) - 3

-8 - 3

-11

Answer:

-11

Step-by-step explanation:

We are given the value of c, so we just need to plug it in. We can do this by replacing "c" with "-2" in our given expression.

4c - 3 ⇒ 4(-2) - 3

Now, we can simplify this.

-8 - 3 = -11

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The equation to model on this situation is :

                   0.6 = (0.75x + 0.9)/(x + 3)

Noemi makes bracelets averaging $0.60 per bead, so we need to write an equation that models this average bead cost. This can be found by dividing the total bead cost by the number of beads used.

1. The total cost of a bead can be found by multiplying the price of each type of bead by the number used and adding these values ​​together.

So:

Total Cost = 0.75x + 3*0.3

                  = 0.75x + 0.9

2. Total number of beads = x + 3

3. Thus, the average cost is:

        (0.75x + 0.9)/(x + 3)

4. Using the value of the average cost per bead given to us ($0.60), we can now write up the full equation:

                      0.6 = (0.75x + 0.9)/(x + 3)

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The complete answer for the verbal expression into an algebraic inequality is  [tex]\frac{n}{-3} +5 \geq 12[/tex] .

What are inequality?

In arithmetic, the relationship between 2 values that are not equal is outlined by inequalities. difference means that not equal. Generally, if 2 values don't seem to be equal, we tend to use “not equal (≠)”.

Main body:

First, let's call "a number": n

"The quotient" means we are dividing.

Therefore, "the quotient of a number and -3" can be written as:

n÷ -3

now we need to add 5 to the expression ,

[tex]\frac{n}{-3} +5[/tex]

The quotient of a number and -3 plus 5 is at least 12.

so the expression found out till is equal to at least 12 which means sign used is " ≥"

Hence , the complete answer is  [tex]\frac{n}{-3} +5 \geq 12[/tex] .

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Answer:

4

6

y=4x+6

Step-by-step explanation:

check the attached file

Answer:

Below

Step-by-step explanation:

If you turn it sideways and use the y-axis portion as the base (4)  , you can see height = 5

Area = 1/2 * b * h =    1/2 *  4 *5 = 10 units^2

(a)     [tex]p_{n} =p_{n-1}-0.4p_{0} +n[/tex]

(b)       [tex]n = {\frac{p_{n-1} -p_{n} }{0.4p_{0}} }[/tex]

Given,

         Initial salmon population [tex]p_{0}=5000[/tex]

         Extraction rate = 40% per year

(a) Formula for recursion,

         For the first year,

                [tex]p_{1} =p_{0} -0.4p_{0}+n[/tex]

         For the second year,

                [tex]p_{2} =p_{1} -0.4p_{0} +n[/tex]

         For the n'th year,

               [tex]p_{n} =p_{n-1}-0.4p_{0} +n[/tex]

(b) The value of n,

        From the above equation,

                [tex]p_{n} =p_{n-1}-0.4p_{0} +n[/tex]

                  [tex]n = {\frac{p_{n-1} -p_{n} }{0.4p_{0}} }[/tex]

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Each year, 40% of the salmon population is extracted from a farming pond.

a. The recursion to describe Pn is Pn = 0.6 Pn-1 + N.

b. The value of N is 3000.

According to the recursion equation, the quantity of fish at the start of the nth year. Pn, is equal to 0.6 times the quantity at the start of the year before, Pn-1, plus the constant quantity of wild salmon that is restocked every year, N.

b. We can set the recursion equation equal to the initial population of 5000 fish in order to get the value of N that ensures the quantity of fish stays constant at the start of each year. Now we have the equation.

0.6Pn-1 + N = 5000. Solving for N gives us N = 3000.

Therefore, a. Pn = 0.6 Pn-1 + N. b.  3000.

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The dimensions that could be the measurements of a similar triangle are; base = 7.8 cm and height = 18 cm

Two triangles are said to be similar provided that they have the same ratio of corresponding sides and an equal pair of corresponding angles.

Now, we are given the side lengths of the triangle as a base length of 3.9 cm and a height of 9 cm.

Thus, this means that a similar triangle will have same ratio of side lengths. Thus;

If new height is h and new base is b, then we have;

9/h = 3.9/b

Thus,

h/b = 9/3.9

If we multiply the right side top and bottom by 2, then we have;

h/b = 18/7.8

18 and 7.8 cm could be similar dimensions.

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The function f(t) = 2cos (∏/4 t) lowest at (4,-2), (12,-2),(20,-2). The points are pl0ted in the graph.

What is a function?

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

Given function is  f(t) = 2cos (∏/4 t).

f(t) will be lowest when cos (∏/4 t) is lowest.

The value of cosine lies between -1 to 1.

When cos (∏/4 t) = -1, f(t) has lowest value.

Solve the equation cos (∏/4 t) = -1

cos (∏/4 t) = -1

∏/4 t =cos ⁻¹ (-1)

∏/4 t = (2n + 1)∏

t = (2n + 1)4  where n is a whole number.

The value of the function is lowest at t = 4, 12, 20.

The lowest points are (4,-2), (12,-2),(20,-2) etc.

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Answer: (4, -2) (12,-2)

Step-by-step explanation:

Evaluating the expression a² + b ÷ 3 for each set of given values we have

The expressions are evaluated using substitution as done below

for a = 4, b=3

substituting the the values of a and b

= a² + b ÷ 3  

= 4² + 3 ÷ 3

= 16 + 1

= 17

For a=2, b=21

substituting the the values of a and b

= a² + b ÷ 3

= 2² + 21 ÷ 3

= 4 + 7

= 11

For a = 3, b = 6

substituting the the values of a and b

=  a² + b ÷ 3

=  3² + 6 ÷ 3

= 9 + 2

= 11

substituting the values yielded the results as 17, 11 and 11

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The Error checking button provides an automatic means of checking for mathematical errors within formulas of a worksheet.

The modeling process begins with the framing of a conceptual model that shows the relationships between the various parts of the problem being modeled.

Arrows pointing from the selected cell to cells that depend on the selected cell are generated by using the Trace dependents button of the Formula Auditing group.

nodes in an influence diagram represent part of the model

The Trace Precedents button, located in the Formula Auditing group, creates arrows pointing to the selected cell from cells that are part of the formula in that cell

The Error checking button provides an automatic means of checking for mathematical errors within formulas of a worksheet.

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To create a  finite-state machine that models an old fashioned soda machine which can perform the stated work we can follow the given steps.

The machine accepts nickels (5 cents), dimes (10 cents) and quarters (25 cents).

Let the states be s , s1 ,s2 ,s3 ,s4 etc.

If we add a nickel to the machine, then the the input is 5 to the current state s , we move them to state s+1 ans so on , and similarly for dime and quarter.

On taking x a the input button for soda pop , we can create the required  finite-state machine that models an old fashioned soda machine that accepts nickels, dimes, and quarters.

A finite-state machine (FSM), sometimes known as a finite automaton  or simply a state machine, is a mathematical model of computation.

It is an abstract machine that can only be in one of a finite set of states at any one moment. In response to some inputs, the FSM can transition from one state to another; this transition is referred to as a transition. An FSM is defined by a set of states, an initial state, and the inputs that cause each transition.

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The six trigonometric functions at 11π/3 are as follows-

sin (11π/3) = -[tex]\sqrt{3}[/tex]/2

cos (11π/3) = 1/2

tan (11π/3) = -[tex]\sqrt{3}[/tex]

cot (11π/3) = -1/[tex]\sqrt{3}[/tex]

sec (11π/3) = 2

cosec (11π/3) = -2/ [tex]\sqrt{3}[/tex]

Let us evaluate the six trigonometric functions at 11π/3 as follows -

11π/3 can be written as (6π+5π)/3 = 2π + 5π/3.

a. sin (11π/3) = sin (2π + 5π/3)

this angle is greater than or equal to 0 and less than 2π.

= sin (5π/3)

Finding the angle with equivalent trigonometric values in the first quadrant. Also, sin is negative in the 4th quadrant.

= -sin (π/3)

= -[tex]\sqrt{3}[/tex]/2

Hence, sin (11π/3) = -[tex]\sqrt{3}[/tex]/2

b. cos (11π/3) = cos (2π + 5π/3)

this angle is greater than or equal to 0 and less than 2π.

= cos (5π/3)

Finding the angle with equivalent trigonometric values in the first quadrant. Also, cos is positive in the 4th quadrant.

= cos (π/3)

= 1/2

Hence, cos (11π/3) = 1/2

c. tan (11π/3) = tan (2π + 5π/3)

this angle is greater than or equal to 0 and less than 2π.

= tan (5π/3)

Finding the angle with equivalent trigonometric values in the first quadrant. Also, tan is negative in the 4th quadrant.

= -tan (π/3)

= -[tex]\sqrt{3}[/tex]

Hence, tan (11π/3) = -[tex]\sqrt{3}[/tex]

d. cot (11π/3) = 1/ tan (11π/3)

Hence, cot (11π/3) = - 1/ [tex]\sqrt{3}[/tex]

e. sec (11π/3) = 1/ cos (11π/3)

Hence, sec (11π/3) = 2

f. cosec (11π/3) = 1/ sin (11π/3)

Hence, cosec (11π/3) = -2/ [tex]\sqrt{3}[/tex]

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