A student is assessing the correlation between the number of workers in a factory of and the number of units produced daily. The table shows the data:
Number of workers
(x)
10 20 30
50 60 70
80
Number of units
(y)
52 102 152 202 252 302 352 402 452
Part A: Is there any correlation between the number of workers in a factory and the number of units produced daily? Justify your answer. (4 points)
Part B: Write a function that best fits the data. (3 points)
Part C: What do the slope and y-intercept of the plot indicate? (3 points)

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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Aftre solving, the all option is false except option c. Only option c, ∅×A=∅ is correct because cartesian product with non empty set with empty set alsways gives empty set.

In the givn question we have to find which statement is true.

To solve the question we let;

A={1,2,3}; B={2,3,4}; C={2,3}

(a) The first option is (A – C) ∩ (A – B) = A – (B ∪ C)

Now solving the both side by putting the value

({1,2,3} – {2,3}) ∩ ({1,2,3} – {2,3,4}) = {1,2,3} – ({2,3,4} ∪ {2,3})

{1} ∩ {1,4} = {1,2,3} – {2,3,4}

{1} = {1,4} (False)

(b) If A ∩ B = ∅, then A ⊂ B

As we know that if If A ∩ B = ∅, then A=∅ and B=∅. That means both A and B will be empty set. So the option B is false.

(c) ∅ X A = ∅

As we know that cartesian product with non empty set with empty set alsways gives empty set. SO the option C is correct.

(d) (A – B) ∪ (B – C) = A – C

Now solving the both side by putting the value

({1,2,3} – {2,3,4}) ∪ ({2,3,4} – {2,3}) = {1,2,3} – {2,3}

{1,4} ∪ {4} = {1}

{1,4} = {1} (False)

(e) ∅ ∩ {∅} = ∅ (False)

(f) B X A = A X B (False)

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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 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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Answer:

Below is a picture

Step-by-step explanation:

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

The range is the set between all of the possible output values, which always shown on y-axis by identify any given domain and then finding the range of any functions is by taking graphs into consideration.

To discover the area and variety, we without a doubt remedy the equation y = f(x) to decide the values of the unbiased variable x and gain the area. To calculate the variety of the feature, we without a doubt explicit x as x=g(y) after which discover the area of g(y).

Because the area refers back to the set of viable enter values, the area of a graph includes all of the enter values proven at the x-axis. The simplest approach of locating the variety of a feature, say y = f(x), is to explicit x as g(y) and pick out the area set for g(y). This might be the variety for the given feature f(x).

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A restaurant chef ha 3/4L of strawberry syrup. He uses 1/40L in each desert that he divide for each and every desert. He made 30 deserts.

Given,

Chef has 3/4l strawberry syrup

Each desert uses 1/40l

To determine no of deserts by divide

= total strawberry syrup / syrup for each desert

= ¾ / 1/40

= 30

No of deserts made = 30

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Answer:

  143

Step-by-step explanation:

You want the value of the term with degree 0 in the polynomial 12x²-42x+143.

The degree of each term is the exponent of the variable. A term with no variables has degree 0.

The term with no variables is also called the constant term. The constant in this polynomial is 143.

The value of the term with degree 0 is 143.

__

Additional comment

If there is more than one variable, the degree of the term is the sum of their exponents.

The outcome of the operation belongs to the same set of domains emphasizing the mean for whole numbers to be closed.

A number system is described as a technique of composing to represent digits. It is the mathematical inscription for describing the numbers of a given set by using numbers or other characters in a uniform method. It delivers a special presentation of every digit and describes the arithmetic structure.

Here,

Closure occurs when an operation on members of a set, such as real numbers, always results in a member of the same set. As a result, the result remains in the same set.

Thus, the outcome of the operation belongs to the same set of domains emphasizing the mean for whole numbers to be closed.

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If discriminant is negative then the nature of roots is imaginary.

For a general quadratic equation, [tex]ax^2+bx+c=0[/tex]

the roots of the equation are [tex]\alpha=\frac{-b-\sqrt{b^2-4ac}}{2a}\ and\ \beta=\frac{-b+\sqrt{b^2-4ac}}{2a}[/tex]

Where, [tex]b^2-4ac[/tex] is known as discriminant.

If

Case i) [tex]b^2-4ac > 0[/tex]

then discriminant is positive and the roots α and β of the quadratic equation  are real and unequal.

Case ii) [tex]b^2-4ac =0[/tex]

then discriminant is zero and the roots α and β of the quadratic equation are real and equal.

Case iii) [tex]b^2-4ac < 0[/tex]

then discriminant is negative and the roots α and β of the quadratic equation are unequal and not real, it means imaginary.

Case iv) [tex]b^2-4ac > 0[/tex] and perfect square

then discriminant is positive and perfect square and the roots α and β of the quadratic equation are real, rational and unequal.

Hence, if discriminant is negative then the nature of roots is imaginary.

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Complex fractions are fractions with a fractional numerator, denominator, or both.

Given,

We have to state about complex fraction;-

Complex fraction;

When both the denominator and the numerator, or both, contain fractions, the fraction is said to be complicated. A complex fraction with a variable is a complex rational expression. For instance: The complex fraction 4/(1/3) has the denominator as 1/3 and the numerator as 4.

Solving the complex fraction;

In the numerator and denominator, make a single fraction. By multiplying the numerator by the inverse or reciprocal of the denominator, you can use the fractional division rule. If it's required, simplify.

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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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Traits can be dominant or recessive, and the recessive traits were obscured by the dominant ones in the F1 generation.

Given,

In the question:

Mendel accounted for the observation that traits which had disappeared in the f1 generation reappeared in the f2 generation by proposing that___

Now, According to the question:

Fill up the above blank:

Mendel accounted for the observation that traits which had disappeared in the f1 generation reappeared in the f2 generation by proposing that__

Solution:

In the Mendel’s experiment, some traits which were absent in the F1 generation appeared in the second generation cross. By this he concluded, that the traits expressed in the F1 generation were dominant and hence they capped the expression of traits associated with recessive allele. He classified the traits in F2 generation as recessive, because these traits can occur only when they are in pair i.e they form individuals with homozygous recessive genotype.  

For instance – If “R” is allele for dominant red color trait and “r” is the allele for recessive white color trait, then the cross between true breeding red flowers and white flowers will produce following offspring  

RR * rr

Rr, Rr, Rr, Rr

Thus, in F1 generation all the offspring are heterozygous red

F2 generation-  

Rr * Rr

RR, Rr, Rr, rr

The recessive trait of white colored flower reappears in second generation.

Hence, Traits can be dominant or recessive, and the recessive traits were obscured by the dominant ones in the F1 generation.

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The required probability that a single reading is between 9 and 12 is 0.2493.

While information focuses are alluded to as x in a typical dissemination, they are called z or z-scores in the z-conveyance. A z-score is a standard score that lets you know the number of standard deviations from the mean a singular worth (x) lies: A positive z-score implies that your x-esteem is more noteworthy than the mean.

Its formula is Z = X - x⁻/S

P(9<x<12)

Z = 12-10/1 = 2 , Z = 8-10/1=-2

Then, P(-2 < Z < 2)  

P(z <2) - (z<-2)

0.4773 - 0.228 = 0.2493

P(-2 < Z < 2)   = 0.2493.

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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

We reject null hypothesis in which there is no difference here between pair of treatment means if the confidence interval for that difference contains zero; this is a "true" statement.

A statistical conjecture known as a null hypothesis asserts that certain features of such a population or content process are not different from one another.

Thus, we reject null hypothesis in which there is no difference here between pair of treatment means if the confidence interval for that difference contains zero; this is a "true" statement.

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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:

Step-by-step explanation:

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

Answer:

18% decrease

Step-by-step explanation:

-Subtract the ending value from the starting value.

40.00 - 32.80 = 7.20

-Divide this number by the starting value.

7.20 / 40.00 = 0.18

-Multiply by 100 to find the percentage change

0.18 * 100 = 18% decrease

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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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.

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 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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Range = 12

■ Maximum value = 10.

■ Minimum value = -2

■ Count of numbers within the set = 13

The number of bacteria that will be there after 3 hours is 6400

What is exponential growth model?

What transpires when you repeatedly multiply by the same amount is described by an exponential growth model. It has a wide range of uses, especially in the economics and life sciences. A population that doubled annually would represent a straightforward exponential growth scenario. For instance, y=A(2)x.

After 1 hour there are 100 bacteria

After 2 hours there are 200 bacteria

Let x be hours and y be the number of bacteria

[tex]y = ab^{x}[/tex]

where, a is initial value and b is growth factor.

After 1 hours, there are 100 bacteria. So, the point is (1,100). Put x=1 and y=100

100 = ab ⇒ (1)

After 2 hours, there are 200 bacteria. So, the point is (2,200). Put x=2 and y=200

200 = ab² ⇒ (2)

Dividing eq (2) and eq(1)

[tex]\frac{200}{100} = \frac{ab^{2} }{ab}[/tex]

b = 2

Putting the value of b in eq 1

100 = 2a

a = 50

When x = 3 what is the y value

y = 50 * [tex]2^{7}[/tex]

  = 50*128

  = 6400

Therefore, the number of bacteria after 3 hours is 6400.

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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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Yes , the 90% confidence interval include the true proportion of youth survey participants who say that they are about the right weight.

The confidence interval for a population proportion is calculated by the  below formula

p ± z×√(p × (1-p))/n

where p is called as sample proportion

z is called as z-value

and n is sample size

Here, we have sample size(n)=100

and by using the z-table we find that p-value=0.56 and z-value=1.645

90% confidence interval=0.56±(1.645×√[0.56×(1-0.56)]/100)

=>90% confidence interval=0.56± [1.645×√(0.56×0.44)/100]

=>90% confidence interval=0.56±[1.645×(√0.2464/100)]

=>90% confidence interval=0.56±[1.645×(0.049)]

=>90% confidence interval=0.56+0.0816 and 0.56-0.0816

=>90% confidence interval=0.6416 and 0.4784

So,90% confidence intervals covers [0.4784,0.6416] proportion of total population.

Here intervals range is greater than zero, it means 90% confidence interval covers the true proportion.

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(Complete question) is:

does the 90% confidence interval include the true proportion of youth survey participants who say that they are about the right weight? If sample size is 100.

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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The entire garden needs to be fence for a total of $156.

Given that,

A fence is required to entirely enclose a garden that is 15 by 24 feet in size. Each foot of fencing costs $2.

To find : The overall cost of fencing the garden?

Dimensions are given by 15 feet and 24 feet

Cost per foot is $2

Total perimeter of garden is given as 2(l+b)

P = 2(l+b)

P= 2(15+24)

P = 78 feet

1 feet = $2

78 feet = 78 * 2 = $156

Therefore, the total cost required to fence the entire garden is $156

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