16. Find the angle between 0 and 2π coterminal with the angle
23π/3

Answer: 3/2

Step-by-step explanation:

3x - 2y = 14

-2y = 14-3x

y = 3/2x-7  divide both sides by -2

Answer:

96

Step-by-step explanation:

21+75

The vertex (3, -16) is the maximum point on our quadratic equation.  

When we compare the given Quadratic function with the general form

ax² +bx +c,    

If the value of a is positive then the Quadratic function will have a minimum value, and the graph of the function opens up.  

If the value of a is negative then the Quadratic function will have a maximum value, and the graph of the function opens downwards.  

Here we have

f(x) = -2(x - 5)(x-7)

f(x) = -2 [x²-7x - 5x + 35 ]

f(x) = -2 [x²-12x + 35 ]

f(x) = -2x² + 12x - 35  

Compare f(x) with ax²+ bx + c  

=> a = -2, b = 12, and c = - 35  

Here,

a = -2 is a negative value then the function f(x) will have maximum value    

And the graph of the function opens down.  

The formula for the x coordinate of the vertex = -b/2a  

The coordinate of x = -(12)/2(-2) = 3    

Now substitute x = 3 in f(x) to find y-coordinate

=> f(3) = - 2(3)² +12(3) - 35    

=> f(3) = -2(9) + 36 - 35          

=> f(3) = - 16    

Therefore, y-coordinate = -16            

Therefore,

The vertex (3, -16) is the maximum point of the quadratic equation.              

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Answer:

375

Step-by-step explanation:

let a garben table cost x

a bench cost x+47

x+x+47=703

2x=703-47

2x=656

x=656÷2=328

bench: 328+47=375

The probability that two cards will be drawn at random, without replacement, is 13/18.

The ratio of good outcomes to all possible outcomes of an event is known as the probability. The number of positive results for an experiment with 'n' outcomes can be represented by the symbol x.

The probability of an event can be calculated using the following formula.

Probability(Event) = Positive Results/Total Results = x/n

In order to better grasp probability, let's look at a straightforward application.

Let's say we need to forecast if it will rain or not. Either "Yes" or "No" is the appropriate response to this query.

There is a chance that it will rain or not. Here, probability can be used. Using probability, one may forecast the results of a coin toss, a roll of the dice, or a card draw.

According to our answer-

P(at least 1 green) = 1 - P(no green)

P(no green) = draw yellow on both draws

= P(draw yellow on 1st draw) * P( draw yellow on 2nd draw, given draw yellow on 1st draw)

= 5/9 * 4/8 = 20/72 = 5/18

P(at least 1 green) = 1 - 5/18

= 13/18

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Answer:

[tex]y=\frac{8}{11} x-3[/tex]

Step-by-step explanation:

Plug in the slope and point into the equation y=mx+b to solve for the y-value of the y-intercept. Plug in the x value for x, the y value for y, and the slope for m.

[tex]5=\frac{8}{11} (11)+b[/tex]

[tex]5=8+b[/tex]

[tex]-3=b[/tex]

After solving that, you can plug the slope and y-intercept back into the equation to solve for y.

[tex]y=\frac{8}{11} x+(-3)[/tex]

[tex]y=\frac{8}{11} x-3[/tex]

Answer:

Step-by-step explanation:

Slope-intercept form is y=mx+b where m is the slope and b is the y-intercept. We have all the information we need except for the y-intercept, so we can plug in our point to solve for the y-intercept.

------------------------------------Solving for y-intercept------------------------------------

Plugging in the point gives us [tex]5=8/11*11+b[/tex]. Simplifying this equation results in [tex]5=8+b[/tex]. To solve for b, we subtract 8 from both sides, giving us that [tex]b=-3[/tex].  We now have both the slope and the y-intercept, so our equation is y = 8/11x -3.

Feel free to contact me with any questions about my answer. I hope this helps!

Yes, the point (2,4) is a solution to the system of inequalities in the graph.

How to solve inequalities?

By definition, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.

The given parameters include

Points (4,2)

y<2x+3

y≥-4x+1

Solving these inequalities

y<2x+3

Let y<0

0<2x+3

-3<2x

x<-3/2

(-3/2,0)

when x<0

y<2(0)+3

y<3

(0,3)

From equation 2

y≥-4x+1

x≥0

y≥0+1

y≥1

(0,1)

y≥0

0≥-4x+1

x≥-1/4

(-1/4,0)

Using the coordinates to draw the graphs the lines cut each other at points where (4,2)

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Answer:

B is a variable it is a letter

5 is a coefficient because it's in front of the variable

3.79 is a term because it is just numbers by itself

Step-by-step explanation:

The equation to determine the number of miles, m, you must run per day is B. 5m + 5.6 = 20; m = 2.88

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. An equation is not the same as a mathematical expression. The equal (=) operator is always used to join two mathematical expressions in an equation.

In mathematics, an equation is a relationship between two expressions that is expressed as an equality on either side of the equal to sign. An equation would be 3y = 16, for instance. Equations can be categorized into one of the following three categories depending on their degree:

In this scenario, the person must run a total of 20 miles per week and ran 5.6 miles in the first two days of the week.

Let the number of miles for the remaining 5 days be m.

This will be:

5m + 5.6 = 20;

Solving for m = will give 2.88.

In conclusion, the correct option is B.

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The fourth degree Taylor polynomial of f(x) centered at 2 the [tex]T_4(2.4) = 11.0225[/tex].

What is Taylor polynomial?

The Taylor series or Taylor expansion of a function in mathematics is the infinite sum of terms expressed in terms of the function's derivatives at one particular point. The function and the sum of its Taylor series are roughly equal for the majority of common functions at this point.

Given:

[tex]f(x) = e^x[/tex]  centered at 2.

[tex]f(2) = e^2[/tex]

[tex]f'(x) = \frac{d}{dx}e^x = e^x , f'(2) = e^2\\f"(x) = \frac{d^2}{dx}(e^x) = e^x, f"(2) = e^2\\ f^3(x) = \frac{d^3}{dx}(e^x) = e^x, f^3(2) = e^2\\ f^4(x) = \frac{d^4}{dx}(e^x) = e^x, f^4(2) = e^2[/tex]

Therefore,

[tex]T_4(x) = f(2) + \frac{f'(2)(x-2)}{1!} + \frac{f"(2)(x-2)^2}{2!} + \frac{f^3(2)(x-2)^3}{3!} + \frac{f^4(2)(x-2)^4}{4!} \\T_4(x) = e^2 [1 + (x - 2) + \frac{(x-2)^2}{2}+\frac{(x-2)^3}{6}+ \frac{(x-2)^4}{24} \\ T_4(2.4) = e^2[1 + (2.4-2) + \frac{(2.4-2)^2}{2}+ \frac{(2.4-2)^3}{6}+\frac{(2.4-2)^4}{24}]\\ T_4(2.4) = 11.0225[/tex]

Hence, the fourth degree Taylor polynomial of f(x) centered at 2 the [tex]T_4(2.4) = 11.0225[/tex].

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The percentage change in the number of visitors = 42.30%.  

The prior value's increase or reduction is indicated by the percentage change. The percentage increase may be used to calculate how much it has increased if the present value exceeds the previous value.

The percentage decline may be used to calculate how much it has reduced if the current value is smaller than the prior value.

The formula for Percentage change in case of increase is given by

Percentage Increase = ( Increase/Original Number) × 100

Here we have

On Monday a museum had 150 visitors

On Tuesday it had 260 visitors

The number of visitors increased from Monday to Tuesday

= 260 - 150 = 110  

By the given formula percentage of change can be calculated as given below

Percentage Increase = (110/260) × 100

= 42.30%

Therefore,  

The percentage change in the number of visitors = 42.30%.  

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The proportional relationship y = 200x, showing the number of calories y burned as a function of the time swimming of x hours, is given as follows:

A proportional relationship is a special case of a linear function, as even though it has a constant rate of change, the intercept is of zero.

The general format of a proportional relationship is given as follows:

y = kx.

In which the constant of proportionality k represents the constant rate of change.

Supposing that for each hour swimming, the person spends 200 calories, the constant is given as follows:

k = 200.

Hence the proportional relationship that gives the number of calories y burned as a function of the time swimming of x hours is given as follows:

y = 200x.

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So the correct statement is A and D

What is a Quadrilateral?

A closed quadrilateral has four sides, four vertices, and four angles. It is a form of polygon. In order to create it, four non-collinear points are joined. Quadrilaterals always have a total internal angle of 360 degrees.

A quadrilateral is a flat shape with four edges and four corners, also known as vertices. The quadrilateral has angles at each of its four vertices, or corners.

The Latin words quadra, which means four, and latus, which means sides, are combined to form the English term quadrilateral. A quadrilateral does not always have to have equal lengths on each of its four sides. 

These are the several kinds of quadrliaterals:

Quadrilateral A'B'C'D' = D8(ABCD) as we know two quadrilateral will be congruent in case of unit length scaling factor and corresponding side length corresponds like AB,BC,CD,DA

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To determine the gain or loss on the redemption of the bonds, you need to compare the redemption price to the carrying value of the bonds. The carrying value of the bonds is the amount that the bonds are recorded as being worth on the issuing corporation's balance sheet. This is calculated by adding the Bonds Payable balance and the Premium on Bonds Payable balance.

In this case, the carrying value of the bonds is $810,000 + $8,910 = $818,910. If the bonds are redeemed at a price of $102, the gain or loss on the redemption can be calculated as follows:

Gain or loss on redemption = Redemption price - Carrying value of bonds

= $102 - $818,910

= -$817,810

Since the gain or loss on the redemption is a negative number, this indicates that the redemption price was lower than the carrying value of the bonds, resulting in a loss. The correct answer is therefore: c. $7,290 loss.

a) The break-even point under the old situation is 680000.

b) The break-even point under the proposed situation is 806451.

c) Birr sales volume must be obtained under the proposed plan to make as much profit as last year is 1129032.

a) The break-even point under the old situation:

100000 * a - 170000 = 1000000 * 8%

a = 25% (Profit rate)

x.a = 170000

x = 680000

b) The break-even point under the proposed situation:

1250000 * b - 170000 -30000 = 80000 + 30000

b = 24.8%

x.b = 20000

x = 806451

c) Birr sales volume must be obtained under the proposed plan to make as much profit as last year :

x.b - 200000 = 80000

x.b = 28000

x = 1129032

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15000 Cls should we expect to include the true mean if we compute the 60% confidence interval for each buffalo count (i.e., data sample).

Given that,

We have to calculate let's now examine the Buffalo's collective data. How many Cls should we expect to include the true mean if we compute the 60% confidence interval for each buffalo count (i.e., data sample).

We know that,

Theoretical hits= confidence interval × total no. of buffaloes

= 0.6×(buffaloes)

Sample hits = count among total no. of buffaloes, from which how many of inside 25000, that will be sample hits.

So,

=0.6×25000

=15000

Therefore, 15000 Cls should we expect to include the true mean if we compute the 60% confidence interval for each buffalo count (i.e., data sample).

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There are 36 possible outcomes when rolling two dice, and only 1 of those outcomes results in a double. Therefore, the probability of rolling a double is 1/36, or approximately 0.028.

If you are willing to pay $20 to roll the dice, then you are effectively paying a premium of $20 for a probability of 0.028 of winning. This means that the expected value of rolling the dice is 0.028 * $20 = $0.56.

Therefore, you should be willing to pay up to $0.56 for the privilege of rolling the dice. Rounded to the nearest cent, this is $0.56.

what do you mean by &?

if its multiplication than

2 × 1/4 = 0.50 or 1/2

4+ (-2) = 2

so the answer is:

2 = 1/2

false

Answer:

Step-by-step explanation:

i need help on that too

The equation of certain hyperbola with center ( -2,0) is (x+ 2)²/25 - (y)²/ 9 = 1

According to the question,

Equation of hyperbola is given : (x-h)²/a² - (y-k)²/b² = 1

Center of hyperbola = (-2,0)

Focus = (-2√34 , 0)

vertex = (-5,0)

This hyperbola is from left to right

As center is (-2,0) means h = -2 and k = 0

Hyperbola are symmetric ,

Second focus = (-2√34 , 0)

Second vertex = ( 5,0)

Vertex are (a,b) => a = 5

Foci of general hyperbola are ( h ± ck)

=> ( h ± c, k) =  (-2√34 , 0)

=> -2 ± c = -2√34

=> c = ± √34

Also , c^2 = a^2 + b^2

=> 34 = 25 + b^2

=> b^2 = 9

=> b = 3

Substituting all the values ,

Equation of Hyperbola is (x+ 2)²/25 - (y)²/ 9 = 1

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The zero's of the polynomial p(x) = x(x² - 9) are -3, 0 and 3.

The zero's of a polynomial p(x) are all the x-values that make the polynomial equal to zero.

In other words, zeros of a polynomial can be defined as the points where the polynomial becomes zero as a whole.

Therefore, let's find the zero's of the polynomial .

p(x) = x(x² - 9)

p(x) = x³ - 9x

0 = x³ - 9x

x³ = 9x

x² = 9

x = √9

Therefore, x = -3 or 3

x  = 0

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Two index that are equivalent to the index (x^{1/3)² are:- 1) X⁽²/³⁾, 2) (∛X)²

What are index ?

An index can be assigned to a number or variable. A value raised to the power of a variable's (or a constant's) value is its index. The exponents or powers are other names for the indices. It displays how many times a particular number must be multiplied. It takes the following form:

a(m) = a × a × a ×……× a (m times)

The base in this case is a, and the index is m.

The index instructs a certain integer (or base) to be multiplied by itself a specified number of times, where the number of times is determined by the index raised to the base. It is a condensed way of expressing large sums of information and calculations.

[tex]X^b . X^A. X^n = X^b^a^n[/tex]

Example: 2^3 = 2 × 2 × 2 = 8

[tex][X^\frac{1}{3} ]^2[/tex][tex]= X^\frac{2}{3}[/tex]

We can also write the same index as;

[tex]A^\frac{1}{n}=\sqrt[n]{A}[/tex]

[tex]X^\frac{2}{3}=[\sqrt[3]{x}]^2[/tex]

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Answer: 59.50=8.25x + 10

Step-by-step explanation: so we know that It is 8.25 per sandwich making it the constant. Then we know that 10 is the the deléguente fee making it the y-intercept. Finally this all has to equal to 59.50. X represents how many sandwiches the person ordered.

Answer:

44

Step-by-step explanation:

80*55/100 = 44

Answer:78

Step-by-step explanation:

The true proportion of the figure based on the triangle proportionality theorem is Option (A).

What is the basic proportionality theorem?

According to the Basic Proportionality Theorem (BPT), if a line is parallel to a triangle's side that divides the other sides into two separate points, the line will divide those sides proportionately.

Given that TU is parallel to QR, by the proportionality theorem, we get

[tex]\frac{ST}{TQ} = \frac{SU}{UR}[/tex]

or, [tex]\frac{k}{j} = \frac{h}{i}[/tex]

or, [tex]\frac{i}{j} = \frac{h}{k}[/tex]

Ans:  [tex]\frac{i}{j} = \frac{h}{k}[/tex]

Hence, a true proportion of the figure based on the triangle proportionality theorem is (A)  [tex]\frac{i}{j} = \frac{h}{k}[/tex]

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The expressions that could represent how much snowfall Delphine had at her house in March will be:

1.4f

f + 0.4f

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.

Since Delphine's house had 40 percent more snowfall than in February. Delphine's house had f centimeters of snowfall in February.

The expression will be:

f + (40% × f)

f + 0.4f

= 1.4f

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Answer: 16

Step-by-step explanation: 16 people can share the pizzas.

Answer: ???

Step-by-step explanation:

You have to put in the numbers for the percentages.

The average change in the height of the rainwater is 1.25 inches per day

What is an Equation of a line?

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

The initial height of the rainwater measured = y₁

The value of y₁ = 24.83 inches

The final height of the rainwater measured = y₂

The value of y₂ = 12.08

The change in height = y₁ - y₂

Substituting the values in the equation , we get

The change in height = 6.75

The number of days = 5 2/5 days

The number of days = 27/5 days = 5.4 days

So , the equation will be

The average change in the height of the rainwater = change in height / number of days

Substituting the values in the equation , we get

The average change in the height of the rainwater = 6.75 / 5.4

The average change in the height of the rainwater = 1.25 inches per day

Hence , the average change is 1.25 inches per day

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The statement "Δ ABD = Δ ACB by SSS" is true about the diagram.

The statement "Δ ABD = Δ ACB by SSS" is true about the diagram. SSS stands for Side-Side-Side, which is a congruence postulate stating that if three sides of one triangle are congruent to the corresponding sides of another triangle, then the triangles are congruent. In the given diagram, Δ ABD and Δ ACB are congruent because their corresponding sides AB, BD, and AC are equal in length.

This means that the triangles have the same shape and size, but they may be oriented differently. The SSS congruence allows us to conclude that all corresponding angles and other corresponding sides of the two triangles are also congruent. Therefore, we can say that Δ ABD is congruent to Δ ACB based on the Side-Side-Side congruence.

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