h Use cubic regression to find a function that fits the following points. (-3, -28) (0, -4) (4, 168) (-5, -174)

Proved that, sin⁴x-cos⁴x/ sin²x-cos²x = 1​.

Here, we have,

given that,

the LHS is:

sin⁴x-cos⁴x/ sin²x-cos²x

now, we know that,

sin²x+cos²x = 1

and, we know that,

a² - b² = (a+b) (a-b)

so, we get,

sin⁴x-cos⁴x/ sin²x-cos²x

= (sin²x+cos²x) (sin²x-cos²x ) / sin²x-cos²x

=(sin²x+cos²x)

=1

= RHS

Hence, Proved that, sin⁴x-cos⁴x/ sin²x-cos²x = 1​

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2-4 is -2 and -5 times -2 is 10 divided by 2 is 5 and 5 +3 is 8. and 8 times 3 is 24. PEMDAS

Answer:

→24

Step-by-step explanation:

Evaluate: {3+[−5(2−4)÷2]}⋅3

= {3+[-5(2-4)÷2]}.3

= {3+[-5(-2)÷2]}.3

= {3+[10÷2]}.3

= {3+[10÷2]}.3

= {3+[10÷2]}.3

= {3+[10/2]}.3

= {3+[5]}.3

= {3+5}.3

= 8.3

= 8*3

= 24 Ans.

Answer:

domain is  

[ 3 , ∞ )

and our range is

( − ∞ , 1 ]

Step-by-step explanation:

Let's look at the parent function:  

√

x

The domain of  

√

x

is from  

0

to  

∞

. It starts at zero because we cannot take a square root of a negative number and be able to graph it.  

√

−

x

gives us  

i

√

x

, which is an imaginary number.

The range of  

√

x

is from  

0

to  

∞

This is the graph of  

√

x

graph{y=sqrt(x)}

So, what is the difference between  

√

x

and  

−

2

⋅

√

x

−

3

+

1

?

Well, let's start with  

√

x

−

3

. The  

−

3

is a horizontal shift, but it is to the right, not the left. So now our domain, instead of from  

[

0

,

∞

)

, is  

[

3

,

∞

)

.

graph{y=sqrt(x-3)}

Let's look at the rest of the equation. What does the  

+

1

do? Well, it shifts our equation up one unit. That doesn't change our domain, which is in the horizontal direction, but it does change our range. Instead of  

[

0

,

∞

)

, our range is now  

[

1

,

∞

)

graph{y=sqrt(x-3)+1}

Now let's see about that  

−

2

. This is actually two components,  

−

1

and  

2

. Let's deal with the  

2

first. Whenever there is a positive value in front of the equation, it is a vertical stretching factor.

That means, instead of having the point  

(

4

,

2

)

, where  

√ 4

equals  2 , now we have  

√ 2

⋅4  equals  2

. So, it changes how our graph looks, but not the domain or the range.

graph{y=2 * sqrt(x-3)+1}

Now we've got that  − 1

to deal with. A negative in the front of the equation means a refection across the  

x -axis. That won't change our domain, but our range goes from  

[ 1 , ∞ )  to  

( − ∞ , 1 ]

graph{y=-2sqrt(x-3)+1}

So, our final domain is  

[ 3 , ∞ )

and our range is  

( − ∞ , 1 ]

The function f(x) = - (x - 2)² + 3 is represents this graph so option (B) will be correct.

A graph is a diametrical representation of any function between the dependent and independent variables.

The graph is easy to understand the behavior of the graph.

For example y = x² form a parabola now by looking at only the graph we can predict that it has only a positive value irrespective of the interval of x.

If a function is graphed then each of its points must satisfy the function.

So we can check putting points on all functions to get to know.

Taking the first function,

f(x) =  (x - 2)² + 3

Now check at points (2,3)

3 ≠  (2+2)² + 3  so this is not satisfying.

It means it is not a function of this graph.

By checking all graphs by all points then we get to know that.

Function,f(x) = - (x - 2)² + 3 is satisfying all points

For example ;

3 = -(2-2)² + 3 = 3

Hence "The function f(x) = - (x - 2)² + 3 is represents this graph".

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The total amount of paper required is 3π(3+√71)unit²

The equation for the surface area of a cone is given as follows:

A = πr²+πrs.

Height of the cone, h = 8 & radius of the cone = 3, the slant height s is given as: s = √(r²+h²)

Substituting the values of r & h to determine s

s = √(8²+3²)

s = √71

Substituting the values to get Area,

A=π*3²+π*3*√71.

A=3π(3+√71)

Hence, the required paper will be A=3π(3+√71)unit²

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a. There are 4 red pens in the box.

b i. Simplifying, we get:

S₄ = 3(x + y) - 2

ii. The fifth term is 4y - 2x + 1.

The chance of an event occurring is called the probability of the event happening. It tells us how likely it is for an event to happen; it does not tell us what is going to happen. There is an even chance of an event happening (happen/not happen).

a. Let the number of non-red pens be n, then we have m + n = 20. Also, after adding 5 more pens, we have m + 3 red pens and n + 2 non-red pens. The probability of selecting two red pens at random without replacement from these 25 pens is given by:

(m + 3)/(20 + 5) * (m + 2)/(20 + 4) = 7/20

Simplifying this equation, we get:

(m + 3)(m + 2) = 14 * 5

Expanding the left side and simplifying, we get:

m² + 5m - 36 = 0

Factoring this equation, we get:

(m + 9)(m - 4) = 0

Since m cannot be negative, we have:

m = 4

Therefore, there are 4 red pens in the box.

b. i. The sum of the first n terms of an arithmetic sequence can be given by:

Sₙ = n/2[2a + (n - 1)d]

where a is the first term, d is the common difference, and n is the number of terms. Using this formula, we can find S₄ as follows:

S₄ = 4/2[x + y + (2x + 1) + (2y - 3)]

= 2(3x + 3y - 1)

= 6(x + y) - 6 - 2

Simplifying, we get:

S₄ = 3(x + y) - 2

ii. The common difference of the sequence is given by:

d = y - x

Therefore, the fifth term can be expressed as:

U₅ = (2x + 1) + 4d

= (2x + 1) + 4(y - x)

= 4y - 2x + 1

Therefore, the fifth term is 4y - 2x + 1.

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a. There are 4 red pens in the box.

b i. Simplifying, we get:

S₄ = 3(x + y) - 2

ii. The fifth term is 4y - 2x + 1.

The chance of an event occurring is called the probability of the event happening. It tells us how likely it is for an event to happen; it does not tell us what is going to happen. There is an even chance of an event happening (happen/not happen).

a. Let the number of non-red pens be n, then we have m + n = 20. Also, after adding 5 more pens, we have m + 3 red pens and n + 2 non-red pens. The probability of selecting two red pens at random without replacement from these 25 pens is given by:

(m + 3)/(20 + 5) * (m + 2)/(20 + 4) = 7/20

Simplifying this equation, we get:

(m + 3)(m + 2) = 14 * 5

Expanding the left side and simplifying, we get:

m² + 5m - 36 = 0

Factoring this equation, we get:

(m + 9)(m - 4) = 0

Since m cannot be negative, we have:

m = 4

Therefore, there are 4 red pens in the box.

b. i. The sum of the first n terms of an arithmetic sequence can be given by:

Sₙ = n/2[2a + (n - 1)d]

where a is the first term, d is the common difference, and n is the number of terms. Using this formula, we can find S₄ as follows:

S₄ = 4/2[x + y + (2x + 1) + (2y - 3)]

= 2(3x + 3y - 1)

= 6(x + y) - 6 - 2

Simplifying, we get:

S₄ = 3(x + y) - 2

ii. The common difference of the sequence is given by:

d = y - x

Therefore, the fifth term can be expressed as:

U₅ = (2x + 1) + 4d

= (2x + 1) + 4(y - x)

= 4y - 2x + 1

Therefore, the fifth term is 4y - 2x + 1.

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If we say that "all left cosets of H have order |H|," it means that every left coset of H has the same number of elements as H, which is the order of the subgroup H.

In group theory, given a subgroup H of a group G, a left coset of H is a subset of G obtained by multiplying every element of H by a fixed element g of G on the left.

The order of a subgroup H is defined as the number of elements in H.

This property of left cosets is important because it allows us to partition the group G into a disjoint union of left cosets of H.

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Step-by-step explanation:

Since DE is parallel to BC, the mL C = 180° -125° = 55°.

so, the measure of L B = 180° - L A - L C =

180° - 60° - 55 = 65°

The measure of angle B is 55 degrees.

When a transversal crosses two parallel lines, alternate interior angles are congruent. In this case, angle DEC and angle B are alternate interior angles since both are formed by the transversal DE intersecting the parallel lines BC and DE. Thus, we have:

Angle B = Angle DEC = 125 degrees.

Now, to find the measure of angle C, we can use the fact that the sum of the interior angles of any triangle is always 180 degrees. So,

Angle C = 180 degrees - (Angle A + Angle B)

Angle C = 180 degrees - (60 degrees + 125 degrees)

Angle C = 180 degrees - 185 degrees

Angle C = -5 degrees.

If we assume that angle DEC is an exterior angle, we can find the measure of angle B as follows:

Angle DEC + Angle B = 180 degrees (since they are supplementary)

125 degrees + Angle B = 180 degrees

Angle B = 180 degrees - 125 degrees

Angle B = 55 degrees.

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Answer:

x intercept: (25,0)

y intercept: (0, -55)

Answer:

y=10

Step-by-step explanation:

you first add 10 to both sides

the bring down the -5y

thr divide it -50 with -5

The answer from part A tells us that the trout population was 10 in the first month after it was introduced.

A. P(0) = 740 / (1 + 73e^-0) = 740 / (1 + 73) = 740 / 74 = 10, so the answer is 10.

B. The answer from part A tells us that the trout population was 10 in the first month after it was introduced.

C. To find the number of trout in the lake after 1 year, we need to find P(12): P(12) = 740 / (1 + 73e^-0.07*12) = 740 / (1 + 73e^-0.84) ≈ 490, so the answer is 490.

D. To find the number of trout in the lake after 10 years, we need to find P(120): P(120) = 740 / (1 + 73e^-0.07*120) = 740 / (1 + 73e^-8.4) ≈ 740, so the answer is 740.

E. lim t→∞ P(t) = 740, so the answer is 740.

F. The answer from part E tells us that as the number of months t approaches infinity, the trout population will approach 740. This means that the trout population will eventually stabilize at 740 if no other factors such as predators, disease, or lack of food affect the population.

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The value of side TS is,

⇒ TS = 28

First, we are going to divide the figure and named new points X and Y as:

Now, we know that TS is the sum of TX and XS.

TS = TX + XS

Additionally, TX has the same length of HJ, so:

TX = HJ = 14

Now, we want to know the length of YK, and we can calculate it using the following equation:

LK = LY + YK

LY = HJ,

so, LY = 14

And, 42 = 14 + YK

42 - 14 = YK

28 = YK

Finally, since T and S are midpoints, the length of XS is the half of the length of YK. It means that XS is:

XS = YK/2

XS = 28/2

XS = 14

Therefore, TS is equal to:

TS = TX + XS

TS = 14 + 14

TS = 28

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Answer: 134/25

Step-by-step explanation:

hope this helps

The probability that a subject would guess more than 20 correct in a series of 36 trials is 0.0001

In a series of 36 trials, if the subject is guessing randomly, then the probability of correctly guessing odd or even is 1/2.

Let X be the number of correct guesses in a series of 36 trials. X follows a binomial distribution with parameters n = 36 and p = 1/2.

The probability of guessing more than 20 correct is:

P(X > 20) = 1 - P(X ≤ 20)

Using a binomial distribution table, we can find that P(X ≤ 20) = 0.9999 (rounded to four decimal places).

Therefore: P(X > 20) = 1 - 0.9999 = 0.0001

So the probability that a subject would guess more than 20 correct in a series of 36 trials is 0.0001 (rounded to four decimal places).

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Answer:

4/15

Step-by-step explanation:

2/5 drive

1/3 bus

and rest walk

fraction of those who walk is 1-(2/5+1/3)

2/5+1/3=(6+5)/15=11/15

15/15-11/15=4/15

Answer: 32

Step-by-step explanation:

4 ÷ 1/8
You can reduce the expression by cancelling out common factors;
4/1 ÷ 1/8
Cross cancel the ones, and then multiply 4 and 8
4 x 8 = 32

The equivalent proportional relationships in this problem are given as follows:

In a proportional relationship, the output variable y is obtained from the multiplication of the input variable x and the constant of proportionality k, by the rule presented as follows:

y = kx.

Proportional relationships are said to be the same when they have the same constant of proportionality k.

For each relationship in this problem, the constants are given as follows:

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On solving the provided question we can say that The following is the data table of the function.

The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.

here,

the provided functions that can be formed are

           x            -infinity < x < -10

f(x) =    2x + 10          -10 < x < 10

           4X - 10       10 < x < infinty

The following is the data table of the function.

x              y

-20          -20

-15          -15

-10          -10

-5             0

0              10

5               20

10              30

15              50

20              70

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An example of the piecewise defined function is: \(f(x)= \begin{cases}x & -\infty < x \leq-10 \\ 2 x+10 & -10 < x \leq 10 \\ 4 x-10 & 10 < x < \infty\end{cases}\)

The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output.

A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or range.

Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.

The following is the data table of the function.

x               y

-20          -20

-15           -15

-10           -10

-5              0

0              10

5              20

10              30

15              50

20             70

The provided functions that can be formed are

\(f(x)= \begin{cases}x & -\infty < x \leq-10 \\ 2 x+10 & -10 < x \leq 10 \\ 4 x-10 & 10 < x < \infty\end{cases}\)

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Since $ASHY$ is a square and $AY=5$, we have $AS=SY=5\sqrt{2}$. Since $ABDC$ is a square and $AB=1$, we have $AC=\sqrt{2}$, so $CY=5\sqrt{2}-\sqrt{2}=4\sqrt{2}$. Finally, since $EFHG$ is a square and $EF=1$, we have $EG=GF=1\sqrt{2}$.

[asy] size(6cm); defaultpen(black+1); pair a=(0,5); pair b=(1,5); pair c=(0,4); pair d=(1,4); pair e=(4,1); pair f=(5,1); pair g=(4,0); pair h=(5,0); pair y=(0,0); pair s=(5,5); draw(a--s--h--y--a); draw(c--d--b,gray); draw(g--e--f,gray); draw(d--y--e--s--d); dot(a); dot(b); dot(c); dot(d); dot(e); dot(f); dot(g); dot(h); dot(y); dot(s); label("$A$",a,NW); label("$B$",b,N); label("$C$",c,W); label("$D$",d,SE); label("$E$",e,NW); label("$F$",f,E); label("$G$",g,S); label("$H$",h,SE); label("$Y$",y,SW); label("$S$",s,NE); label("$1$",(a+b)/2,N); label("$\sqrt{2}$",(c+d)/2,N); label("$1\sqrt{2}$",(e+f)/2,N); label("$5$",(a+s)/2,W); label("$5$",(s+h)/2,E); label("$5\sqrt{2}$",(a+s)/2,NE); label("$5\sqrt{2}$",(s+h)/2,NW); label("$4\sqrt{2}$",(s+y)/2,NW); [/asy]

We can now compute the area of quadrilateral $DYES$ by subtracting the areas of triangles $DYE$ and $YES$ from the area of square $DESY$.

We have $[DYE]=\frac{1}{2}\cdot DY\cdot YE=\frac{1}{2}\cdot(4\sqrt{2})\cdot(5\sqrt{2}-1)=38-2\sqrt{2}$ and $[YES]=\frac{1}{2}\cdot YS\cdot ES=\frac{1}{2}\cdot(5\sqrt{2})\cdot(1\sqrt{2})=\frac{25}{2}$.

The area of square $DESY$ is $(DY+YE)^2=(4\sqrt{2}+5\sqrt{2}-1)^2=100-18\sqrt{2}$. Thus, the area of quadrilateral $DYES$ is \begin{align*}

[DESY]-[DYE]-[YES]&=\left(100-18\sqrt{2}\right)-\left(38-2\sqrt{2}\right)-\left(\frac{25}{2}\right)\

&=61-\frac{49}{2}\sqrt{2}.

\end{align*}Therefore, the area of quadrilateral $DYES$ is $\boxed{61-\frac{49}{2}\sqrt{2}}$.

Answer:

B

Step-by-step explanation:

Standard deviation is the average distance away from the mean, thus B is correct

Answer:

the probability of rolling a sum of 6 with these dice is 1/6.

Step-by-step explanation:

To find the probability of rolling a sum of 6 with the given pair of dice, we can first list all possible pairs of outcomes that add up to 6:

(2,4)

(3,3)

(4,2)

For each of these pairs, we need to find the probability of rolling each number on its respective die and then multiply those probabilities together. The probability of rolling a particular number on one die is the number of times that number appears on that die divided by the total number of outcomes on that die.

For the first pair (2,4), the probability is:

(2 appears twice on one die out of six possible outcomes) × (4 appears once on the other die out of six possible outcomes) = (2/6) × (1/6) = 1/18

For the second pair (3,3), the probability is:

(3 appears twice on one die out of six possible outcomes) × (3 appears twice on the other die out of six possible outcomes) = (2/6) × (2/6) = 4/36

For the third pair (4,2), the probability is:

(4 appears twice on one die out of six possible outcomes) × (2 appears twice on the other die out of six possible outcomes) = (2/6) × (2/6) = 4/36

The total probability of rolling a sum of 6 is the sum of the probabilities of each possible pair:

1/18 + 4/36 + 4/36 = 1/6

Therefore, the probability of rolling a sum of 6 with these dice is 1/6.

The probability of drawing a king from a standard deck of 52 cards is 1/13.

In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.

To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).

The total number of possible outcomes is 52 because there are 52 cards in the deck.

The favorable outcomes, in this case, are the four kings.

Therefore, the probability of drawing a king is given by:

Probability = (Number of favorable outcomes) / (Number of possible outcomes)

= 4 / 52

= 1 / 13

Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.

This means that out of every 13 cards drawn, on average, one of them will be a king.

It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.

Each draw is independent, and the probability of drawing a king is constant.

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The area of trapezoid DEFG having coordinates D (2, 3), E (4, 3), F (6, 1), and G (2, 1) is found to be  12 square units.

The diagram is attached for the question.

Area of trapezoid DEFG = 1/2(sum of parallel sides)*height

Area of trapezoid DEFG = 1/2*(2 + 4)*4

Area of trapezoid DEFG = 12 square units

Thus, the area of trapezoid DEFG having coordinates D (2, 3), E (4, 3), F (6, 1), and G (2, 1) is found to be  12 square units.

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If tan x=sin x/cos x then, tan(90-A)=1/tan A

tan ( 90-A ) = \(sin(90-A)/cos(90-A)\)

since  sin (90-A) = cos A

and cos (90-A) = sin A

So  \(tan(90-A)=sin(90-A)/cos(90-A)=cosA/sinA\)

cos A/Sin A=cot A

\(cot A=1/tan A\)

Therefore, tan(90-A)=1/tan A

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The reading on the scale in part (a) is 11.0 kg, in part (b) is 5.5 kg, and in part (c) is 16.5 kg.

a) The reading on the scale will be 11.0 kg. This is because the mass of the salami is supported by the cord, which is then measured by the spring scale. The force exerted by the salami on the spring is equal to the weight of the salami, which is equal to the mass times the acceleration due to gravity (F = ma = mg). Therefore, the reading on the scale will be equal to the mass of the salami (11.0 kg).

b) The reading on the scale will be half of 11.0 kg, or 5.5 kg. This is because the weight of the salami is being supported by two cords, one running from the salami to the pulley and one running from the pulley to the wall. The force exerted by the salami on the scale is equal to the weight of the salami (F = mg). Since the force is now being shared between two cords, the force exerted on the scale is only half the weight of the salami (F = mg/2). Therefore, the reading on the scale will be 5.5 kg.

c) The reading on the scale will be 16.5 kg. This is because the two salamis are now being supported by one cord, which runs from one salami to the other and then to the scale. The force exerted by the salamis on the scale is equal to the sum of the weights of both salamis (F = mg₁ + mg₂). Therefore, the reading on the scale will be equal to the sum of the masses of both salamis (16.5 kg).

The reading on the scale in part (a) is 11.0 kg, in part (b) is 5.5 kg, and in part (c) is 16.5 kg.

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Step-by-step explanation:

a= c-b pls let me know if it is correct or not

The derivative of the function cos(xº) in radians is y' = -sin(xπ/180)

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

cos(xº)

Changing the degree into radian, we have

cos(xπ/180)

Express as a function

So, we have

y = cos(xπ/180)

When the cosine function is differentiated, we have

y' = -sin(xπ/180)

Hence, the differentiated function is y' = -sin(xπ/180)

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Reason:

tan = opposite/adjacent

tan(D) = EF/DE = d/f

tan(F) = DE/EF = f/d

Comparing d/f with f/d, and we find they are reciprocals. The two fractions multiply to 1.