How do you tell if the degree of a polynomial is even or odd from a graph?.

The three steps for finding the mean absolute deviation are - i)Find the mean of the given observations, ii)Find difference between each observation and calculated mean, iii)Evaluate the mean of the differences obtained in the second step.

Absolute deviation is somewhat same with mean deviation in some extent. The measurement of spread represents the amount of dispersion in a data-set, that is how spread-out are the values of data-set around the central value(example- mean/mode/median).It tells how far away the data points to fall from the central value.

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Using the Induction hypothesis,

strong induction that every integer greater than 1 can be written as the product of primes

Induction Hypothesis:

This is the assumption that given a general element a[n], if something is true about the elements of an ordered set, we can show that it is also true for a[n+1]. is. This means it must be true for all elements. A classic example is the proof that the sum of the natural numbers is triangular.

Induction Has Strong and Weak Versions

This is a case where strong induction is needed because factoring n gives no information about the factorization of n+1.

For brevity, we say that even prime numbers are products of prime numbers. So the statement is: "Every number n≥2 is a product of primes". So the steps are:

base case, where we prove n=2.

If n>2 and every number m with 2≤m prove that n is also a product of primes. The

base case is because 2 is prime.

Let n>2. If n is prime, we are done. Otherwise, n=ab and 1 products of prime numbers.

Strong Induction: Base Case: n=2 and n has a factor of 1.2 n is prime:

Assume k is prime or can be expressed as the product of sets of prime factors for all k≤n To do.

We need to show that n+1 is prime or that n+1 can be expressed as the product of a set of prime factors.

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The number of sweets that Dave have equals to 18 sweets.

In mathematics, a ratio is a metric that shows how many times one number contains another. For instance, if we have 8 oranges and 6 lemons in a bowl of fruit, then, the ratio of oranges to lemons is eight to six. Similarly, the ratio of lemons to oranges is 6:8 and the ratio of oranges to the total amount of fruit is 8:14.

Given data

Dave and martin ratio = 2:3

Dave is given 15 sweets.

The number of sweets that dave have now is computed as follows:

2/5 = 0.4= 40%

3/5 = 0.6 = 60%

Dave sweets will equals to:

= 15 sweets + (15 sweets * 1/5)

= 15 sweets + 3 sweets

= 18 sweets.

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A triangle field has sides that are 6:7:8 and a perimeter of 420 meters.

Hence, A triangle field has sides that are 6:7:8 and a perimeter of 420 meters.

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The computed probability is computed as <0.8967, 0.1033> which shows that as the days 90 by, the probability of rain on the current day increases monotonically towards a fixed point.

Chance is the branch of arithmetic concerning numerical descriptions of how probable an event is to occur, or how probable it is that a proposition is proper. The chance of an event is a range between zero and 1, wherein, roughly speaking, 0 indicates the impossibility of the occasion and 1 shows actuality. The higher the chance of an occasion, the much more likely it's miles that the event will occur. A simple example is the tossing of a truthful (impartial) coin. because the coin is truthful, the two outcomes ("heads" and "tails") are both similarly possible; the chance of "heads" equals the possibility of "tails"; and on account that no different effects are feasible, the possibility of either "heads" or "tails" is half off (that could additionally be written as zero.5 or 50%).

these standards had been given an axiomatic mathematical formalization in chance ideas, that are used extensively in areas of observation which include records, arithmetic, technology, finance, gambling, artificial intelligence, gadget studying, computer science, sport idea, and philosophy, for example, draw inferences about the expected frequency of events. possibility concept is likewise used to describe the underlying mechanics and regularities of complex structures.

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The required value Z = 11.792 >1.96 at a 0.05 level of significance.,he null hypothesis is rejected,the alternative hypothesis is accepted at a 0.05 level of significance.

As the mean weight is less than 16 ounces.

Given that the mean of the Population = 16

Given that the standard deviation of the process

σ = 0.03 ounce

Given that the mean of the sample = 16.05 ounces

Null hypothesis: H₀:μ > 16 ounces

Alternative HypothesisH₁: μ <16 ounces

    Z = x-mean/SD/√n      

    Z = 16.05-16/0.03/√50

    Z =  11.792

Level of significance = 0.05

Z₀.₀₅ = 1.96

The required Z = 11.792 >1.96 at 0.05 significant level,null hypothesis is rejected and alternate hypothesis is accepted.

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The ratio of the depth of the liquid to the depth of the cup is 4/5.

Geometry and Ratio

The formula for the volume of a cone is:

[tex]V=\frac{1}{3}\pi r^{2}h[/tex]

where r is the radius of the base of the cone and h is the height of the cone.

When the conical cup is filled with water, there will be a difference in the radius of the water and the cup and a difference in the height of the water and the height of the cup (can be seen in the picture).

From the difference in radius and height of the water with the conical cup, a ratio can be made of similarity rule of triangle (see picture).

If the radius of water is [tex]r_{1}[/tex] and the height of water is [tex]h_{1}[/tex], radius of cup is [tex]r_{2}[/tex] and the height of cup is [tex]h_{2}[/tex], so:

[tex]\frac{r_{1} }{r_{2} } =\frac{h_{1} }{h_{2} }[/tex]

[tex]r_{1}[/tex] with [tex]r_{2}[/tex] and  [tex]h_{1}[/tex] with  [tex]h_{2}[/tex] have the same certain ratio. Let's assume the ratio is x, then it can be written:

[tex]r_{2}=x.r_{1} \\h_{2}=x.h_{1}[/tex]

The ratio of the volume of water to the volume of the conical cup is 64/125, meaning that 64 of the water in the conical cup with a volume of 125.

From here we can substitute it in the volume ratio:

[tex]\frac{V_{1} }{V_{2}}=\frac{\frac{1}{3}\pi r_{1}^{2}h_{1} }{\frac{1}{3} \pi r_{2}^{2}h_{2}} =\frac{64}{125} \\\frac{V_{1} }{V_{2}}=\frac{\frac{1}{3}\pi r_{1}^{2}h_{1} }{\frac{1}{3} \pi (xr_{1})^{2}(x.h_{1})} =\frac{64}{125} \\\frac{V_{1} }{V_{2}}=\frac{\frac{1}{3}\pi r_{1}^{2}h_{1} }{\frac{1}{3}\pi r_{1}^{2}h_{1}x^{3} } =\frac{64}{125} \\\frac{V_{1} }{V_{2}}=\frac{1}{x^{3}}=\frac{64}{125}\\ \frac{1}{x^{3}}=\frac{64}{125}\\\\x^{3}=\frac{125}{64} \\x=\frac{5}{4}[/tex]

The ratio between the radius and height of the cup and the water is 5/4. This means that the ratio between the radius and height of the water and the cup is 4/5.

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Answer:

Step-by-step explanation:

The sum of the measures of the angles of a triangle is 180°.

m<D + m<E + m<F = 180°

4x + 2x + m<F = 180

What is the measure of <F? It's not clear in the post.

Answer:

a) 14

b) 13

Step-by-step explanation:

P= Purse W= Watch

1P + 1W = 27 (So think about different combinations that make 27)

2P + 1W = 41 (Multiply this by negative 1)

So now you have

1P + 1W = 27

-2P - 1W = -41

You can subtract them

-1P = -14 or 1P = 14

So 1 purse = 14

Now plug it in

14 + 1W = 27 (Subtract 14 from both sides)

1W = 13

So 1 watch = 13

Furthermore, 1 watch = 13 and 1 purse = 14

Answer:

Below is a picture

Step-by-step explanation:

Demos is a free calculator that can do things like this for you.

[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &\pounds 679\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ t=years\dotfill &3\\ \end{cases} \\\\\\ A=679(1 - 0.04)^{3} \implies A=679(0.96)^3\implies A \approx 600.74[/tex]

The value of the phone after 3 years is equal to £600.73

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate the percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word percent means per 100. It is represented by the symbol “%”

Given here, the present value of the phone is £679 and we are required to find the future value of the phone after 3 years when it depreciates every year by 4%

thus, FV= £679 × (1-4%)³

             =  £679 × 0.96³

             = £600.73

Hence The value of the phone after 3 years is equal to £600.73

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3x² - 7x + 9 is x² - 11x + 17 less than 2x² + 4x - 8.

The value of the expression, x² - 11x + 17, when x = 2 is: -1.

To find the value of an expression, simply replace the given value of the variable and solve to simplify.

To find how much less the expression, 3x² - 7x + 9 is less than 2x² + 4x - 8, subtract 2x² + 4x - 8 from 3x² - 7x + 9:

(3x² - 7x + 9) - (2x² + 4x - 8)

3x² - 7x + 9 - 2x² - 4x + 8

Combine like terms

x² - 11x + 17

Substitute x = 2 into the expression:

2² - 11(2) + 17

= -1.

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Answer:

Step-by-step explanation:

6m+15=36-m

Plus m to both sides

7m+15=36

Minus 15 from both sides

7m=14

Divide by 2

m=2

The fewest number of bags DeShawn must buy to cover Field A is 6.5 bags.

A circle's area is the area that it takes up in a two-dimensional plane. It can be simply calculated using the formula A = r², (Pi r-squared), where r is the circle's radius. The square unit, such as m2, cm2, etc., is the unit of area. Area of a circle is equal to r² or d²/4, where = 22/7 or 3.14. A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle has rotational symmetry around the center.

Given,

DeShawn needs grass seed to cover Field A. One bag of grass seed covers `5000` square feet.

Field A is a circular field with a `100`-foot radius.

Area of circular field:

Area = πr²

Where r = 100

Area = 3.14 × 100²

Area = 31400 square feet

Each bag seeds cover 5000 square feet,

So, dividing area by 5000

5000÷ 31400

6.28

The fewest number of bags DeShawn must buy to cover Field A is 6.5 bags.

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Remainder formula helps us to find the remainder when total number of possible sequence of games (i.e 3452) is divided by 1000.

The Remainder is 432.

We have given that

Number of players in team A = 7

Number of players in team B = 7

This problem is the same as the number of combinations problem. Let's assume team A is the winner (and we must remember to multiply our final result by 2 to account for the possibility that B is the winner).

A can win exactly 6 of the first k+6 games, and then Game k+7 (ending the series in exactly k+7 games), in (k+66) = (k+6k) ways, so we want

2∑k=06(k+6k).

This is 2⋅(1+7+28+84+210+462+924)= 3432.

Conversely, given a permissible series, allow the losing team to win all of the remaining (unplayed because superfluous) games, and you end up with a 7-7 tie.

Now, we calculate the remainder when 3432 is divided by 1000.

Using Remainder Formula ;

Dividend = Divisor × Quotient + Remainder

3432 = 1000× 2 + 432

so, remainder is 432 .

Hence , toatal number of possible sequence of games is 3432.

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Using Relative frequency formula ,

We can easily compute the relative frequency missing terms in given table.

the missing terms in relative frequency are 0.14,0.2,0.26

Relative frequency:

Relative frequency can be defined as the number of occurrences of an event divided by the total number of events occurring in a given scenario.

To calculate the relative frequency,

Relative frequency = f / n

Creating a relative frequency table is a two-step process:

we have given a table of values of experiment results carried by Nimah .

we have to find out the relative frequency for given data .

total frequency= 10+11+15+17+20 = 75

dropping

toat piece frequency relative frequency

3 10 10/75 = 0.13

4 13 11/75= 0.14

5 15 15/75= 0.2

6 17 17/75 = 0.22

7 20 20/75 = 0.26

Hence, we computed the relative frequency table for given data.

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Complete question:

Niamh carrie out an experiment dropping piece of toat to ee if they land jam up or jam down. Here are her reult. Complete the miing relative frequency value in the table. (1 mark)

total frequency terms are 75 .

given data :

dropping

toat piece frequency relative frequency

3 10 0.13

4 13

5 15

6 17 0.22

7 20

The properties of a vector space are satisfied Properties 1,2, 5(a) and 5(c) are satisfied, the relaxation of the homes aren't legitimate are if[tex]v = x ^ 2 1× v=1^ ×x ^ 2 = 1 #V[/tex]

Property three does now no longer follow: Suppose that Property three is legitimate, shall we name[tex]v = a * x ^ 2 +bx +c[/tex]the neuter of V. Since v is the neuter, then O have to be constant with the aid of using the neuted, consequently [tex]0 = O + v = (O x ^ 2 + Ox + O) + (a × x ^ 2 + bx + c) = c × x ^ 2 + b ^ 2 + a[/tex]

= 0 If O is the neuter, then it ought to restore x², but [tex]0+ x² = (0x²+0x+zero) + (x²+0x+zero) = 1.[/tex]This is a contradiction due to the fact x² isn't 1. We finish that V doesnt have a neuter vector. This additionally method that belongings four would not observe either. A set with out 0 cant

have additive inverse

[tex]Let r= v ×2x ^ 2 + v × 1x +v0 , w= w ×2x ^ 2 + w × 1x +w0 . We have that\\v+w= (vO + wO) ^ x^ 2 +(vl^ × wl)^ x+ ( v 2^ × w2)• w+v= (wO + vO) ^x^ 2 +(wl^ × vl)x+ ( w 2^ ×v2)[/tex]

Since the sum of actual numbers is commutative, we finish that v + w = w + v Therefore, belongings 5(a) is valid.

Property 5(b) isn't valid: we are able to introduce

a counter example. we could use z = 1 then[tex]v = x ^ 2 w = x ^ 2 + 1\\(v + w) + z = (x ^ 2 + 2) + 1 = 3x ^ 2 + 1[/tex]

v + (w + z) = x ^ 2 + (2x ^ 2 + 1) = x ^ 2 + 3

Since 3x ^ 2 +1 ne x^ 2 +3. then the associativity rule doesnt hold.

[tex](1+2)^ * (x^ 2 +x)=3^ * (x ^ 2 + x) = 3x + 3\\1^ × (x^ 2 +x)+2^ × (x ^ 2 + x) = (x + 1) + (2x + 2) = 3x ^ 2 + x ( ne 3x + 3 )\\(1^ ×2)^ ×(x^ 2 +x)=2^ × (x ^ 2 + x) = 2x + 2\\1^ × (2^ × (x ^ 2 + x) )=1^ × (2x+2)=2x^ 2 +2x( ne2x+2)[/tex]

Property f doesnt observe because of the switch of variables. for instance, if v = x ^ 2 1 × v=1^ × x ^ 2 = 1 #V

Properties 1,2, 5(a) and 5(c) are satisfied, the relaxation of the homes arent legitimate.

Step-with the aid of using-step explanation:

Note that each sum and scalar multiplication entails in replacing the order from that most important coefficient with the impartial time period earlier than doing the same old sum/scalar multiplication.

Property three does now no longer follow: Suppose that Property three is legitimate, shall we name v = a × x ^ 2 +bx +c the neuter of V. Since v is the neuter, then O have to be constant with the aid of using the neuted, consequently[tex]0 = O + v = (O × x ^ 2 + Ox + O) + (a × x ^ 2 + bx + c) = c × x ^ 2 + b ^ 2 + a[/tex]

= zero If O is the neuter, then it ought to restore x², but zero [tex]+ x² = (0x²+0x+zero) + (x²+0x+zero) = 1.[/tex]This is a contradiction due to the fact x² isn't 1. We finish that V doesnt have a neuter vector. This additionally method that belongings four would not observe either. A set with out 0 cant have additive inverse

Let [tex]r= v × 2x ^ 2 + v × 1x +v0 , w= w2x ^ 2 + w × 1x +w0 . \\We have thatv+w= (vO + wO) ^ x^ 2 +(vl^ wl)^x+ ( v 2^ w2)w+v= (wO + vO) ^ x^ 2 +(wl^ vl)x+ ( w 2^v2)[/tex]

Since the sum of actual numbers is commutative, we finish that v + w = w + v Therefore, belongings 5(a) is valid.

Property 5(b) isn't valid: we are able to introduce

a counter example. we could use[tex]z = 1 then v = x ^ 2 w = x ^ 2 + 1(v + w) + z = (x ^ 2 + 2) + 1 = 3x ^ 2 + 1v + (w + z) = x ^ 2 + (2x ^ 2 + 1) = x ^ 2 + 3\\Since 3x ^ 2 +1 ne x^ 2 +3.[/tex]then the associativity rule doesnt hold.

Note that each expressions are same because of the distributive rule of actual numbers. Also, you could be aware that his assets holds due to the fact in each instances we 'switch variables twice.

[tex]· (1+2)^ * (x^ 2 +x)=3^ * (x ^ 2 + x) = 3x + 31^ * (x^ 2 +x)+2^ * (x ^ 2 + x) = (x + 1) + (2x + 2) = 3x ^ 2 + x ( ne 3x + 3 )(1^ * 2)^ * (x^ 2 +x)=2^ * (x ^ 2 + x) = 2x + 21^ * (2^ * (x ^ 2 + x) )=1^ ×* (2x+2)=2x^ 2 +2x( ne2x+2)[/tex]

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Answer:

SSS: Side-Side-Side

AAS: Angle-Angle-Side

SAS: Side-Angle-Side

ASA: Angle-Side-Angle

Step-by-step explanation:

These are all used for triangles and proofs :)

Answer:

12

Step-by-step explanation:

Number of outcomes for a coin = 2

Number of outcomes of a die = 6

2*6 = 12

Quadratic functions are one type of non linear function.

Given,

We have to find whether quadratic function non-linear;

The graph is not a straight line if it is non-linear. A non-linear function has a curved line as its graph. A line that continuously changes in direction is said to be curved.

These are the so-called nonlinear functions, and they can take many various shapes. A quadratic function is one of these nonlinear functions, and its typical form is y = ax2 + bx + c. A parabola represents the graph of a quadratic function.

Therefore,

Quadratic functions are one type of non linear function.

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The doubles fact for 7 8 is 7+7+1=15.

In simple words, Double Plus One Fact is a strategy for adding two consecutive numbers . To get final result then simply add a smaller number to itself or double it then and add 1.

The numbers that are added together are known as doubles. For example, 5+5=10, 3+3=6, so the doubles plus one fact are simply adding 1 to the resultant of the double fact.

For given, the doubles fact is 7+7=14, then add 1 to get 15.

As a result, 7+7+1=15 is the doubles fact for 7 8.

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Side Angle Side(SAS) , theorem can be used to prove that ABC is congruent to DCA.

According to our question-

The SAS congruency theorem,

two triangles are congruent if any pair of corresponding sides and their included angles are identical in both triangles. In this scenario,

the pair of corresponding sides AB with DC and AD with DA

and their included angles BAD with CDA are equal.

Hence, Side Angle Side(SAS) , theorem can be used to prove that ABC is congruent to DCA.

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The total cheese production in 2006 was about 7.7 billion pounds and the total cheese production in 2014 was about 9.7 billion pounds

The equation of the function is given as

y = 7(1.03)ˣ

From the question, we understand that:

x represents the number of years after 2003

So, we calculate x when the year is 2006 using

x = 2006 - 2003 = 3

Substitute x = 3 in the equation y = 7(1.03)ˣ

y = 7(1.03)³

Evaluate the equation

y = 7.7 (approximately)

We calculate x when the year is 2014 using

x = 2014 - 2003 = 11

Substitute x = 11 in the equation y = 7(1.03)ˣ

y = 7(1.03)¹¹

Evaluate

y = 9.7 (approximately)

Hence, the amount of cheese is 9.7 billion pounds

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The slope of the line in the simplest form is 1 / 2.

The slope of a line is the change in the dependent variable with respect to the change in the independent variable.

The slope is rise over run.

The slope of the line can be found as follows:

m = slope = y₂ - y₁ / x₂ - x₁

Therefore, using (7, 0) and (3, -2)

Hence,

x₁ = 7

x₂ = 3

y₁ = 0

y₂ = -2

Therefore,

slope = - 2 - 0 / 3 - 7

slope = - 2 / -4

slope = 1 / 2

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Parallel lines Examples from Real Life

Parallel lines are straight lines that never meet each other no matter how long we extend them. Observe the following figure that shows parallel lines.

Numerous pairs of angles are created when a transversal line intersects any two parallel lines. While some angles are complementary, others are congruent (equal).

Hence we get the required answer.

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The correct answer is that B and C both have constant torque.

a)The torque about the left side (i.e -1)

T = (8-28-3)c/4= -232/4.

b)The torque about the left side (i.e -1)

T = (8+24-12-20)c/4 = 0

c) The torque about the left side (i.e -1)

T = (20+60-80)c/4 = 0

d)The torque about the left side (i.e -1)

T = (24-6-12-8)c/4 = -2c/4

The net force is the vector sum of forces appearing on a particle or object. The net pressure is a single force that replaces the impact of the unique forces on the particle's movement. It gives the particle equal acceleration as all the one's real forces together as described by Newton's second law of motion.

The internet pressure is whilst a body is in motion and plenty of forces are energetic on it like gravitational force [tex]F_{g}[/tex], frictional pressure [tex]F_{f}[/tex], and the everyday force. consequently, the net force formula is given by way of.[tex]F_{Net}[/tex] = [tex]F_{a}[/tex]+ [tex]F_{g}[/tex] + [tex]F_{f}[/tex] + [tex]F_{N}[/tex].The net force is the vector sum of all the forces appearing on an item. while an object is in equilibrium (either at rest or shifting at a regular pace), the net pressure acting on its miles is 0. The greater the net force performing on the object, the greater its acceleration will be. Newton's second law of movement summarizes those relationships. The equation for acceleration above can be rewritten to solve for net force as internet pressure = Mass ×Acceleration, or F = m × a.

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Answer:

1. Distribute

2. Combine like terms

3. Get all variable on one side and everything else on the other (Inverse operations: Add / subtract)

4. Solve for one of your variables (inverse operation: Multiple / Division

5. Simplify

Answer:

Step-by-step explanation:

are there values for f or b or q? What are we trying to solve?