y/-2 = -34
giving brain.

There is enough evidence to conclude that Mrs. Smith and Mrs. Jones are not equally effective teachers.

At the null hypothesis, it is tested if the means are the same, hence:

[tex]H_0: \mu_1 - \mu_2 = 0[/tex]

At the alternative hypothesis, it is tested if the means are different, hence:

[tex]H_0: \mu_1 - \mu_2 \neq 0[/tex]

For each sample, the mean and the standard error are given as follows:

Hence the mean and the standard error for the distribution of differences are given as follows:

The test statistic is given by the division of the mean by the standard error of the distribution of differences, hence:

z = -7/3.5119

z = -1.99.

We have a two-tailed test, as we are testing if the mean is different of a value.

Using a z-distribution calculator, with z = -1.99, and a two-tailed test, the p-value is given as follows:

0.0466.

As the p-value is less than the standard significance level of 0.05, there is enough evidence to conclude that Mrs. Smith and Mrs. Jones are not equally effective teachers.

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The the experimental probability of rolling the given result that a number more than 3 is D. 0.44

Probability simply means the chance that a particular thing or event will happen. It is the occurence of likely events. It is simply the area of mathematics that deals with the numerical estimates of the chance that an event will occur or that a particular statement is true.

The following observations can be gotten based on the information:

1 = 32

2 = 36

3 = 44

4 = 20

5 = 30

6 = 38

Therefore, probability = sum of observation (3,4 and 5) / total no of observation

= 20 + 30+ 38 / 200

= 88 / 200

= 0.44

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A die is rolled 200 times with the following results. Outcome 1 2 3 4 5 6 Frequency 32 36 44 20 30 38 What is the experimental probability of rolling the given result? a number more than 3 a. 0.88 c. 0.56 b. 0.34 d. 0.44 Please select the best answer from the choices provided A B C D

The probability for possibilities of x between P(X>4) and P(6.72<X<10.16)  is 0.5987 and 0.2351

X is N(5, 16)

means that, Z=(x-mean)/√variance = (x-5)/√4

=(x-5)/2

that is, Z is standard normal.

Then, by symmetry of the standard normal curve,

P(X>4)=P(X−5>4−5)

=P(X−54>4−54)

= P(Z>−14)

=P(Z>−.25)

=P(Z<.25)

= 0.5987.

Similarly

P(6.72<X<10.16)

= P(6.72−5<X−5<10.16−5)

=P(6.72−54<10.16−54)

=P(0.43<Z<1.29)

=P(Z<1.29)−P(Z<.43)

=.9015−.6664

= 0.2351.

Therefore, The probability for possibilities of x between P(X>4) and P(6.72<X<10.16)  is 0.5987 and 0.2351

Complete question - X is a normal random variable with mean=5 and variance=4 What are the possibilities for P(X>4) and P(6.72<X<10.16)?

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First of all remember that all triangles are always equal to 180 degrees from that we can figure out that x is is 70 because 30+80+70=180. z would be 40 because it is parallel to 40 and therefore equal to it. y is 100 because 40+40+100=180. Recap:

x: 70

z: 40

y: 100

c.The graph of G(x) is the graph of F(x) stretched vertically flipped over the x axis and shifted 4 units to the left.

A diagram that depicts the relationship between two variables, usually measured along opposite axes in a pair is known as graph.

Here,

Given :

Suppose that F(x) = x² and G(x)

compares the graph of G(x) with the graph of F(x)

-(x+4)².

Thus , the solution by observing the given information is:

So, it is

C.The graph of G(x) is the graph of F(x) stretched vertically flipped over the x axis and shifted 4 units to the left.

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Since the ordered pair (a, b) satisfies the inequality y > x + 3, a statement which is true include the following: C. b is greater than a.

In Mathematics, an ordered pair is sometimes referred to as a coordinate and it can be defined as a pair of two (2) data points or elements that are commonly written in a fixed order within parentheses as (x, y).

This ultimately implies that, an ordered pair is typically used for representing the x-coordinate or x-axis (abscissa) and the y-coordinate or y-axis (ordinate) on the coordinate plane of any graph.

Based on the given ordered pair (x, y) which satisfies this inequality y > x + 3, this can be rewritten in terms of a and b as follows;

y > x + 3

b > a + 3

In this context, we can reasonably infer and logically deduce that b is greater than a i.e b > a.

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Complete Question:

The ordered pair (a, b) satisfies the inequality y>x+3. Which statement is true?

A.if you add 3 to b , it will equal a

B. a is greater than b

C. b is greater than a

D. If you subtract 3 from b, it will equal a

Answer:

3. f(3) = 16

4. h(3) = 4

Step-by-step explanation:

3.

f(x) = x² + 7

f(3) = 3² + 7

f(3) = 16

4.

h(x) = 12/x

h(3) = 12/3

h(3) = 4

Answer:

3/20.

Step-by-step explanation:

The solution's f[x] means f(x)=0 when x is not in [−2,2]

The answer to [-2,2] is: f(x)dx=P(X∈dx)=2∗(2−|x|)dx4∗(12∗2∗2)=14(2−|x|)dx

Consequently, f(x)=14(2|x|) on [2,2]

and if not, f(x)=0

For [2,0], it is 14(2+x), while for [2,0], it is 14(2-x).

I discovered a formula for the uniform distribution U=X for (a,b), however, I don't believe this is right since the answer would then be X+24 without X being an absolute value. It also doesn't apply to other questions of a similar nature.

Please assist; there is a very strange exercise question in the textbook that we are unable to solve on our own. I have no idea how they obtained the 2(2|x|)dx4(12|2]).

Furthermore,  f(x) may indicate f(x)=0 when x is not in [2,2].

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The Full question would be:

Consider a point picked uniformly at random from the area inside the shape with the coordinates (-2,0), (0,2), (2,0), (0,-2).

Answer: -1/2

Step-by-step explanation:

Therefore the slope of the line passes through  (5, 9) and (3, -5) comes out to be 7.

By computing the ratio of the vertical to horizontal distance (rise over run) between two points, the slope—a numerical value that defines how steep a line is—is often calculated.a number that indicates how inclined a line is, is frequently determined by dividing the vertical distance (rise over run) between two places by the horizontal distance (run over rise).

The slope of line that passes through  (5, 9) and (3, -5)

Slope= gradient between the two points

Slope= (y2-y1)/(x2-x1)

Where y2= -5

Y1= 9

X2= 3

X1= 5

(-5-9)/(3-5)

-14/-2

7

Therefore the slope of the line passes through  (5, 9) and (3, -5) comes out to be 7.

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Answer: Synthetic division and synthetic substitution are both methods used to divide polynomials, but they are used for different types of polynomials and have different steps and procedures.

Synthetic division is a method used to divide a polynomial by a linear binomial of the form (x-c), where c is a constant. It is used to find the quotient and remainder of the division, and it involves a process of simplifying the polynomial using a specific set of steps.

Synthetic substitution, on the other hand, is a method used to divide a polynomial by a polynomial of higher degree. It is used to find the quotient and remainder of the division, and it involves replacing a variable in the polynomial with an expression and then simplifying.

In summary, Synthetic Division is used when dividing a polynomial by a linear binomial and Synthetic Substitution is used when dividing a polynomial by a polynomial of higher degree.

Step-by-step explanation:

Synthetic division is used for polynomial division by a linear factor, resulting in a quotient polynomial. Synthetic substitution, however, is used to find the value of a polynomial function at a given x-coordinate.

Synthetic division and synthetic substitution are both methods used in algebra to evaluate polynomials. However, they differ in their specific applications and the outcomes they provide.

Synthetic division is a method used to divide a polynomial by a linear factor of the form (x - c). It allows for quick and efficient division without the need for long division. The process involves setting up a synthetic division table and performing a series of calculations based on the coefficients of the polynomial. The result is a simplified quotient polynomial.

On the other hand, synthetic substitution is a technique used to evaluate a polynomial function at a specific value of x. It involves substituting the given value into the polynomial and using synthetic division to perform the calculations. The result obtained is the value of the polynomial at that particular x-coordinate.

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The distance travelled by larger circular wheel is 2π(R-r) more than the distance travelled by old tires.

What is a circle?

A circle is a special kind of ellipse in which the eccentricity is zero and the two foci are coincident. A circle is also termed as the locus of the points drawn at an equidistant from the center. The distance from the center of the circle to the outer line is its radius. Diameter is the line which divides the circle into two equal parts and is also equal to twice of the radius.

The equation of circle in the plane is given as:

(x-h)^2 + (y-k)^2 = r^2

where (x, y) are the coordinate points

(h, k) is the coordinate of the center of a circle

and r is the radius of a circle.

and Area of circle = πr²

Circumference of circle=2πr

Now

let radius of old tires =r

radius of new tires =R

distance travelled by new tire in one rotation= 2πR

distance travelled by old tire=2πr

Hence,

            The distance travelled by larger circular wheel is 2π(R-r)  more than the distance travelled by old tires.

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The correct statement based on the number line is,

⇒ √68 is to the right of Point Q because it is greater than 8.

Number line is a horizontal line where numbers are marked at equal intervals one after another form smaller to greater.

Given that;

The number line showing numbers from -8 to 8 in increments of 2, has point P at 0, and point Q is at 8.

Now, We know that;

⇒ √68 = 8.24

And,

⇒ 8.24 > 8

Hence, √68 is to the right of Point Q because it is greater than 8.

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Answer: it’s 25

Step-by-step explanation:

15 +10

The value of the evaluated iterated integral is 0.1202.

As per the given data the iterated integral is [tex]I & =\int_0^1 \int_0^{s^6} \cos \left(s^7\right) d t d s[/tex].

Here we have to evaluate the given iterated integral.

The definite integral of a real-valued function f(x) with respect to a real variable x on an interval [a, b] is expressed as[tex]$\int_a^b f(x) d x$[/tex] = F(b) - F(a)

Here,

[tex]$\int=$[/tex] Integration symbol

a = Lower limit

b = Upper limit

f(x) = Integrand

dx = Integrating agent

Thus, [tex]$\int a b f(x) d x$[/tex] is read as the definite integral of f(x) with respect to d x from a to b.

Indefinite integrals are implemented when the boundaries of the integrand are not specified.

[tex]I & =\int_0^1 \int_0^{s^6} \cos \left(s^7\right) d t d s[/tex]

Integrate the given iterated integral.

We get:

[tex]& =\int_0^1 \cos \left(s^7\right)\left(\int_0^{s^6} d t\right) d s[/tex]

[tex]& =\int_0^1 \cos \left(s^7\right) \times[t]_0^{s^6} d s . \\[/tex]

[tex]& =\int_0^1 \cos \left(s^7\right) \times\left(s^6-0\right) d s . \\[/tex]

[tex]& =\int_0^1 s^6 \cos \left(s^7\right) d s[/tex]

Say [tex]s^7=t[/tex]                 when s = 0

[tex]\Rightarrow \frac{d t}{d s}=7 s^6 \quad$[/tex]                          t = 0  

[tex]\Rightarrow \frac{d t}{7}=s^6 d s[/tex]              when s = 1.....   t = 1

Replace the assumed terms.

Then we get:

[tex]$I=\int_0^1 \cos (t) \frac{d t}{7}$[/tex]

[tex]$=\frac{1}{7} \int_0^1 \cos (t) d t$[/tex]

[tex]$=\frac{1}{7}[\sin (t)]_0^1=\frac{1}{7}[\sin (1)-\sin (0)]$[/tex]

[tex]=\frac{\sin (1)}{7}$[/tex]

[tex]\int_0^1 \int_0^{s^6} \cos \left(s^7\right) d t d s[/tex] = 0.1202

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The two factors of the first number 28 that their sum is will be equal to the second number 16 are 2 and 14.

Factor is a number that divides another number without a remainder. That is if multiplying two whole numbers gives us a product, then the numbers we are multiplying are factors of the product.

The first number 28 have the following factors:

1, 2, 4, 7, 14, and 28.

the factors 2 and 14 are the factors we need because;

2 × 14 = 28

2 + 14 = 16

Therefore, 2 and 14 are the two factors of 28 that their product is the first number 28 and their sum is the second number 16.

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The length of the one of the leg of the triangle is 12√2 in. Thus, option B is correct.

The longest side of a right triangle in geometry is called the hypotenuse. Moreover, it is the side that faces the right angle. The definition of hypotenuse is "length under" or "stretch under." Plato was said to have used it for the first time around 400 BC.

In many applications of geometry and trigonometry, the hypotenuse plays a significant role. The Pythagorean Theorem is the most widely known. Using the Pythagorean Theorem, a2 + b2 = c2, one can determine the length of the hypotenuse.

The Right angles triangle is also a isosceles angled triangle which means two of the angles are equal.

When two angles are equal the corresponding sides are equal too.

a = b

Given that the measure of the triangles' hypotenuse is 24 inches

c² = a² + b²

24² = a² + b²

576 = a² + b²

But the sides are equal i.e.

a = b

Giving us

576 = a² + a²

576 = 2a²

a² = 576/2

a² = 288

a = √288

a = 12√2

Thus, the length of the one of the leg of the triangle is 12√2 in. Thus, option B is correct.

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Answer:

Step-by-step explanation:

b e2020

Since there is a 0.45 chance of winning a prize at the carnival game, the likelihood that he will win one is 0.04 out of every five games.

Probability theory, a subfield of mathematics, analyzes the likelihood that an event will occur or a statement is true. The probability of an event occurring is a number between 0 and 1, where approximately 0 indicates how unlikely the event is and 1 indicates how certain it is. A probability is a quantitative expression of the likelihood that a particular event will occur. Probabilities can also be expressed as percentages between 0% and 100% or as percentages between 0 and 1. the ratio of the total number of outcomes to the number of events in a complete collection of equally likely outcomes that result in a certain occurrence.

given

= (0.45 )* 1*5 / 5

= 0.04

Since there is a 0.45 chance of winning a prize at the carnival game, the likelihood that he will win one is 0.04 out of every five games.

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For the m/m/1 queuing model, the average number in the system is equals to the four. So, the correct answer is option (c).

This is the most widely used queuing system in analytics. M/M/1 is a good approximation for a large number of

mass service systems. The M/M/1 quening system assumes a Poisson arrival process. This assumption is a very good approximation for the process of arriving at real systems that satisfy the following rules,

We have, customer service is every 4 minutes. So, the Service rate μ = 1 customer/4 minutes = 0.25 customer/minute or 15 per hour.

Customers arrive individually at a rate of one customer every 5 minutes according to the distribution of poisons.

Number of customer service= 1

The arrival rate is 1/ (mean time between arrivals) . Here, the rate of arrival of customers/5 minutes is λ = 0.2 customers/min or 12 per hour. Therefore,

Utilization factor = (arival rate /service rate)100 = λ/μs

Utilization factor = (12/15) 100%

= (4/5)100 = 80%

Utilization factor = 80%

Average number in the system = λ/( μ - λ)

= (60/5)/[ (60/4)-(60/5)]

= 12/3 = 4

So, the average number in the system is 4.

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Complete question:

A queuing model that follows the m/m/1 assumptions. a customer can be served every 4 minutes. customers arrive independently at the rate of one customer every 5 minutes according to a poisson distribution. the average number in the system is

a) 7

b) 5

c) 4

d) 6

The value of p and w in the triangle are 6 units and 13√3 units respectively

Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.

In the triangle, we have angles of 30° and 90°

Using trigonometric ratios:

sin 30° = (2p+1)/(6p-10)     [sin = opp/hyp]

1/2 = (2p+1)/(6p-10)

1/2(6p-10) = (2p+1)

3p -5 = 2p + 1

3p -2p = 1+5

p = 6 units

cos 30° = w/(6p-10)       [cos = adj/hyp]

(√3)/2 = w/(6p-10)

(√3)/2 = w/((6×6) -10)

(√3)/2 = w/(36 -10)

(√3)/2 = w/26

w = (√3)/2 × 26

w = 13√3 units

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The number of sides that the polygon has is given as follows:

24 sides.

A regular polygon is a polygon in which all side lengths have the same measure, hence all the internal angles of the polygon will also have the same measure.

The sum of the internal angle measures of a polygon of n sides is given as follows:

S(n) = (n - 2) x 180º.

For a regular polygon of n sides, with n angles of equal measure, the measure of each interior angle is given as follows:

I = (n - 2) x 180/n.

In the case of the center of the polygon, the sum of the internal angles is of 360º, hence the number of sides n can be obtained as follows:

n  = 360/I.

For this problem, the internal angle measure is given as follows:

I = 15º.

Hence the number of sides is calculated as follows:

n = 360/15

n = 24 sides.

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By taking the quotient between the total amount that she makes and the time of work, we will see that the rate of payment is $45 per hour.

The rate of payment is equal to the quotient between the amount she is paid and the time in which she works.

We know that Theresa wins $0.03 per word, and she can write 3000 words in 2 hours.

Then the amount that she wins is:

$0.03*3000 = $90

Then the rate of payment is:

$90/2 hours = $45 per hour.

Theresa wins 45 dollars per hour.

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Answer: To find the X and Y components of the 15N weight of the birthday cake, we can use trigonometry. We know that the angle of inclination of the table is 23° above the horizontal.

We can use the tangent function to find the X component of the weight, which is the component that is parallel to the table.

X = 15N * tangent (23°)

We can use the sine function to find the Y component of the weight, which is the component that is perpendicular to the table.

Y = 15N * sine (23°)

By applying these formulas and plugging in the angle and weight we can find the respective X and Y components.

Step-by-step explanation:

Using the concept of ratio and proportions, the number of employees in A and B restaurant are 0.72 and 0.28

The relationship between two amounts of the same kind or that are linked is known as a proportion. It is used to compare the magnitude of one quantity to another and is typically expressed as a ratio or fraction. A percentage in mathematics is an equation proving the equality of two ratios.

In this problem, we have a total of 25 employees.

18 out of the 25 employees what to go to restaurant A.

The proportion of this is calculated as

18 / 25 = 0.72

Also, we have 7 employees that want to go to restaurant B

This is calculated as;

7 / 25 = 0.28

The proportion of employees that want to go to restaurant A and B are 0.72 and 0.28 respectively

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Complete Question:

A group of 25 employees want to go out for a group dinner.

18 employees want to go to Restaurant A.

7 employees want to go to Restaurant B.

Use this information to answer the questions below.

What is the proportion of employees who want to Restaurant A and B

To prove this statement, we will use the following definitions and properties:

A finite dimensional vector space is a vector space that has a finite number of basis vectors.

A basis for a vector space is a set of vectors that span the space, meaning that any vector in the space can be written as a linear combination of the basis vectors.

A linear combination of a set of vectors is an expression of the form a_1v_1 + a_2v_2 + ... + a_nv_n, where v_1, v_2, ..., v_n are the basis vectors and a_1, a_2, ..., a_n are scalars from the field.

A non-zero element of a finite dimensional vector space is a vector that is not equal to the zero vector, the additive identity of the space.

Now, let's assume that V is a finite dimensional vector space over a field F, and let B be a basis for V. We will show that every non-zero element of V can be expressed as a unique linear combination of the basis vectors in B.

Let v be a non-zero element of V. Since B spans V, there exists a set of scalars a_1, a_2, ..., a_n from the field F such that v = a_1v_1 + a_2v_2 + ... + a_nv_n, where v_1, v_2, ..., v_n are the basis vectors in B. This is a valid linear combination representation of v with respect to B.

To show that this linear combination representation of v is unique, let's assume that there exists another set of scalars b_1, b_2, ..., b_n from the field F such that v = b_1v_1 + b_2v_2 + ... + b_nv_n. Then, subtracting the second equation from the first one, we get:

0 = (a_1 - b_1)v_1 + (a_2 - b_2)v_2 + ... + (a_n - b_n)v_n.

Since B is a basis for V, the only way for the left-hand side of the equation to be the zero vector is for all the scalars in the linear combination to be equal, i.e. a_1 = b_1, a_2 = b_2, ..., a_n = b_n. Thus, v can be expressed as a unique linear combination of the basis vectors in B, which completes the proof.

i. α = 56°

ii. adj =  4.1

iii. opp = 2.79

We have to recall that what makes the right angle triangle unique is the fact that one of the angles that we find in the triangle is 90 degrees. We have to recall that the sum of the angles that we have in a triangle is 180°.

Hence we have;

α = 180 - (90 + 34)

α = 56°

Then;

Cos 34 = adj/5

adj = 5 cos 34

= 4.1

Sin 34 = opp/5

opp = 5 * sin 34

= 2.79

These are the parts of the right angled triangle required.

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Answer: W = 7

Step-by-step explanation:

do PEMDAS and then follow the order of operations rule