The length of a rectangle is 8
meters and the width is 4 meters
Find the perimeter of the
rectangle

Answer:

find the tan inverse

[tex] { \tan(?) }^{ - 1} [/tex]

of the value to get the angle.

1d.p = 29.2°

Answer:

p = 10

Step-by-step explanation:

4 ^ 10 x 4 ^ 5 = 4 ^ 10+5 = 4 ^ 15

p = 10

The system has been balanced using lean techniques to meet the takt time as much as possible and the facility works 1 shift of 8 hours with two 15 min breaks, so the daily demand is 2700 units / day.

In the given question, the system has been balanced using lean techniques to meet the takt time as much as possible and the facility works 1 shift of 8 hours with two 15 min breaks.

We have to find the daily demand.

The figure is given below:

Total operating time of the facility = 8 hours - 2 breaks of 15mins each

Total operating time of the facility = 480 mins - (2*15 mins)

Total operating time of the facility = 480 mins - 30 mins

Total operating time of the facility = 450 minutes.

Time taken for 1 output = Cycle time of system = Bottleneck of the supply-demand matched process = 10 seconds.

Total output = Total operating time / Time taken for 1 output

Total output = 450 minutes / 10 seconds

Total output = 2700 units / shift.

Since the market's demand and operational time are in balance, all production is created using the pull principle.

That means; Supply = demand.

Therefore the market demand for the product = 2700 units / day.

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the average amount of time spent watching television per week has decreased from the previous mean of 20.8 hour then the test is left tailed

In two tailed hypothesis, the alternative hypothesis is when mean can either be lesser or greater than the given value. Usually uses the symbol ≠.

In right tailed, the alternative hypothesis is when the mean is greater than the given value.

In left tailed, the alternative hypothesis is when the mean is lesser than the given value.

In this question, the hypothesis test to be performed is to determine if the average amount of time spent watching television per week has decreased from the given value of 20.8 hours.

Thus, it is left tailed test.

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The two column proof for the statemen is as follows

Statement                                         Reason

2(-x + 4) = 3                                      given

-2x + 8 = 3                                         Distributive property of multiplication

-2x = 3 - 8                                          Collection of similar terms

-2x = -5                                              Subtraction property of equality

-2x/-2 = -5/-2                                     Division property of equality

x = 5/2                                               Definition of equality

The area of mathematics known as algebra is used to portray situations or problems using mathematical expressions.

In algebra, we utilize integers with fixed or definite values, such as 2, 13, 0.5, etc. combined with variables like x, y, and z

An instance of algebra is 2( -x + 4) = 3

The distributive property of multiplication is applied when there is multiplication over addition of terms like exemplified here

2(-x + 4)

= -2x + 4

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Answer: 6

Step-by-step explanation:

(P.S.: Everything in italics are numbers.)

So the answer will be 6! You're welcome!

Four special two digit numbers exist: 1, 2, 145, and 40585.

A special two-digit number is one in which the original two-digit number is equal to the sum of the number's digits plus the product of its digits. Take the number's initial and last digits out, then add and multiply each digit independently. After that, multiply the two-digit number by the sum and product of its digits and then compare the result to the original value. If they match, it qualifies as a special two-digit number; otherwise, it does not.

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Two triangles if the side between any two corners of one triangle cornor corresponds to the side between the corresponding two angles of the second triangle corner are said to be congruent by the ASA rule.

Create a point F' on ray AC such that BF' is equal to DE.

Angle BAF' = angle BAC, which equal to

angle EDF, AB = DE (given), so ∆ DEF

= ∆ ABP

Point F' has two possibilities: F' is equal to point C please.

If F' is not on C, line AC and ray BC intersect only at C, so F' is not on ray BC. Therefore the angle ABF' is not = the angle ABC. But this is a contradiction. Because angle ABF' = angle DEF (because ∆ DEF = ∆ ABF') and angle DEF = angle ABC (given). So, this case does not occur.

Therefore, F' = C must be true.

∆ABC = ∆ABF' = ∆DEF.

The reasonwe only need some parts to

prove congruence of triangles is that from these parts we can (in Euclidean geometry) derive other parts. This is because the basic axioms and definitions allow us to make "guesses" that turn out to be true every time.

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If the length of a rectangle is increasing at a rate of 3 cm/s and its width is increasing at a rate of 5 cm/s. The area of the rectangle increasing is:  114 cm2/sec.

Using product rule formula

(dA / dt) = L× (dW / dt) + W × (dL / dt)

Where:

dA/dt = Rate that the area of the rectangle is increasing

dL/dt = 3 cm/s

L = 15 cm

dW/dt = 5 cm/s

W = 13 cm

Let plug in the formula

(dA / dt) = (15) × (5) + (13) × (3)

(dA / dt) = 75 + 39

(dA / dt)  = 114 cm2/sec

Therefore 114 cm2/sec is the area of the rectangular.

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the test statistic z is 1.7

What is test statistic?

A test statistic may be a datum employed in applied math hypothesis testing. A hypothesis take a look at is often laid out in terms of a test statistic, thought of as a numerical outline of a data-set that reduces the info to at least one worth that may be wont to perform the hypothesis test.

Main body:

Calculate the test statistic using the formula:

z= [tex]p-p'[/tex]/[tex]\frac{p'(p-p')}{n}[/tex]

where:

p = sample proportion,

n = sample size, and

Po =  population proportion under the null hypothesis

Sample size = 34 websites = n

Sample proportion = 0.20 = p'

z = (0.3 - 0.2)/ (0.2*0.1)/34

z = 0.1 *34/0.02

z = 1.7

Hence value of test statistic z is 1.7

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The rational root theorem says that if you take all the factors of the constant term in a polynomial and divide by all the factors of the leading coefficient

The rational root theorem is also known as the rational zero theorem (or) the rational zero test (or) rational test theorem and is used to determine the rational roots of a polynomial function.

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The correct option is that Undergraduate is assigned to the purchaser group.

P ( purchase | Undergraduate ) = [tex]\frac{70}{70 + 30}[/tex] = 70 / 100 = 0.70 ,

                                         ⇒   P ( y = 0 | Undergraduate ) = 0.3

P ( purchase | Graduate ) = [tex]\frac{100}{100 + 110}[/tex] = 0.476

                                         ⇒   P ( y = 0 | Graduate ) = 0.524

Therefore,

    as P ( y = 1 | undergraduate ) = 0.707 >  0.30 and

                                                       0.476  > 0.524,

Undergraduate group is assigned to the purchase group.

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An example of rational roots can be given as:

Let the polynomial be: 4x³ + 3x² + 6x + 9;

Then,

coefficient of the variable with the highest degree = 4

coefficient having the variable with degree 0 = 9

Factors of 4 are: 1, 2;

Factors of 9 are: 1, 3;

The possible rational roots for such an equation will be: 3, 1, 1/2, 3/2, -3, -1, -1/2, -3/2;

Rational roots are the roots or solutions of equations of any polynomial consisting of one variable of any power.

Where all the coefficients are integers.

Let the solution/root of a polynomial be p/q. Then the root would be rational if and only if the coefficient of the variable with the highest degree is divisible by 'q' , and the coefficient independent of the variable or having the variable with degree 0 is divisible by 'p'

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Integers greater than 0 are positive number.

What is rational number?

A rational number could be a number that may be expressed as the quotient or fraction p/q of 2 integers, a dividend p and a non-zero divisor letter.

Main body:

The definition of positive integers in math states that "Integers that are larger than zero are positive integers". Integers may be classified into 3 types: negative integers, zero, and positive integers. examine the quantity line given below to know the position and worth of positive integers.

1 is that the smallest positive whole number and therefore the greatest positive whole number isn't referred to as the list is endless.

Therefore the definition of positive integer is such as.

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The explicit formula for a sequence given in the form of a₁ , a₂ , a₃ representing initial terms 5,10,20, 40 , 80 , 160 , 320 then aₙ = 5 × 2ⁿ⁻¹.

As given in the question,

Given initial terms of the sequence are as follow:

5, 10, 20, 40, 80, 160, 320

a₁ , a₂ , a₃ representing initial terms

a₂ / a₁ = 10 /5

         = 2

a₃ / a₂ = 20 /10

          = 2

a₄ /a₃ = 40 / 20

        = 2

Common ratio 'r ' = 2

First term a₁ = 5

Given sequence is representing the geometric sequence

Explicit formula for nth of the  geometric sequence is given by :

aₙ = a₁ × rⁿ⁻¹

    = 5 × 2ⁿ⁻¹

Therefore, the explicit formula for a sequence given in the form of a₁ , a₂ , a₃ representing initial terms 5,10,20, 40 , 80 , 160 , 320 then

aₙ = 5 × 2ⁿ⁻¹.

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Answer:

No solution.

Step-by-step explanation:

1. Move terms to the left side

x² - 3x = -8

x² - 3x - (-8) = 0

2. Use the quadratic formula

x = [tex]\frac{-b + \sqrt{b^2 - 4ac} }{2a}[/tex]

Once in standard form, identify a, b, and c from the original equation and plug them into the quadratic formula.

x² - 3x + 8 = 0

a = 1

b = -3

c = 8

x = [tex]\frac{-(-3) + \sqrt{(-3)^2 - 4 * 1 * 8} }{2*1}[/tex]

3. Simplify

After simplifying:

x = [tex]\frac{3 + \sqrt{-23} }{2}[/tex]

4. No real solutions because the discriminant is negative.

The square root of a negative number is not a real number.

d = -23.

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The equation to represent the hanger diagram is   5x - 2x = 21 - 12 and weight of 1 triangle in the hanger is 3 gram. .

In the question ,

it is given that ,

the the weight of one square is = 2 gram

the weight of one circle is = 3 gram

and the weight of one triangle is is = x gram

When the hanger is balanced , then weight on Left side =  weight on Right side

we see that left side have 2 triangles , 6 squares and 3 circles ,

and the Right side have 2 circle , 3 square and 5 triangle ,

So , the balanced equation for the hanger can be written as

2*x + 6*2 + 3*3 = 2*3 + 3*2 + 5*x

2x + 12 + 9 = 6 + 6 + 5x

2x + 21 = 12 + 5x

5x - 2x = 21 - 12

3x = 9

x = 3

Therefore , the equation is 5x - 2x = 21 - 12  and the weight of triangle is 3 grams .

The given question is incomplete , the complete question is

There is a hanger that is in balance. squares are worth 2 grams and circles are worth 3 grams, and triangles are x grams. write an equation to represent the hanger diagram and find the weight of 1 triangle .

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The weight that is left when 18759 grams of bricks are removed is 3.241 kg

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

Pile of bricks = 22 kg

The weight removed from the pile = 18759 grams

The remaining weight can be calculated using the following subtraction equation

Remaining weight = Pile of bricks - The weight removed from the pile

Substitute the known values in the above equation, so, we have the following representation

Remaining weight = 22 kg - 18759 grams

Convert grams to kg

This gives

Remaining weight = 22 kg - 18.759 kg

Evaluate the difference in the above equation

Remaining weight = 3.241 kg

Hence, the remaining weight is 3.241 kg

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The inequality shown in the diagram is the one in option C.

-2 < x ≤ 7

On the number line we can see that our variable is x, the graph of the solution set of the inequality starts with an open circle at x = -2.

The open circle means that x = -2 is not a solution of the inequality, then we start with:

-2 < x

Then we can see a closed circle at x = 7, a closed cirlce means that the value is a solution, so x can be equal to 7, and the inequality is:

-2 < x ≤ 7

So the correct option is C.

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The difference between any two successive integer squares is equal to the total of all these two integers, as demonstrated by the completed proof.

Let x represent any integer to prove algebraically.

This means that x+1 should be the following integer.

The claim demands evidence;

(x+1)² - x² = x+(x+1)

Consider the left hand side;

= x² + x + x + 1² - x²

= 2x+1 (Left Hand Solution)

Similarly, the right side.

= x + (x + 1)

= 2x + 1

Thus, subtracting the difference between two consecutive squared integers equals adding the two integers that since LHS=RHS equality is clear.

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Product of first 10 natural numbers is 3628800.

What is natural numbers?

In arithmetic, the natural numbers are those numbers used for enumeration and ordering. Numbers used for enumeration are referred to as cardinal numbers, and numbers used for ordering are referred to as ordinal numbers

Main body:

The first ten natural numbers are 1,2,3,4,5,6,7,8,9,10.

The product is the multiple all numbers.

Product of first 10 natural numbers is given by,

P = 1*2*3*4*5*6*7*8*9*10

P =3628800.

Therefore, Product of first 10 natural numbers is 3628800.

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The exact difference from (-4, 2) to (4, 6) is √80 units

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

(-4, 2) to (4, 6)

These points can be rewritten as

(x, y) =  (-4, 2) to (4, 6)

The exact difference can be calculated using the distance formula

distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Where

(x, y) =  (-4, 2) to (4, 6)

Substitute the known values in the above equation, so, we have the following representation

distance = √[(-4 - 4)² + (2 - 6)²]

Evaluate

distance = √80

Hence, the distance is √80 units

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The inequality to represent the number of album and song Jorge can download is 2s + 12a ≤ 50

It cost 2 dollars to download a song and 12 dollars to download an entire album. Jorge has 50 dollars to spend on downloading music.

The inequality that represents the number of songs(s)  and album(a) that Jorge can download can be represented as follow:

Therefore,

Hence, the inequality is as follows:

2s + 12a ≤ 50

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Answer: 39 in

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

2 * 6

6 + 6 = 12

Answer:

12

Step-by-step explanation:

At the zero point the curve can either cross the x-axis or just touch it. The root of the function is the number c with f(c) = 0.

If the graph intersects the x-axis and looks nearly linear at the intersection, it is a single root. Even multiplicity zero if the graph touches the x-axis and bounces off the axis.

Different graphs with different x-intercepts. The graph may intersect the x-axis at the intersection. Otherwise, the graph touches the x-axis and bounces.

For example, suppose you plot a function.

f (x) = (x + 1) (x - 2)²

See the figure above to see how the function behaves differently for different x intercepts.

x intercept at x = -1 is the solution of the equation

x + 1 = 0 , graph goes straight through the x intercept at x= −1 . We call it a single zero because zero corresponds to a single factor in the function.

x intercept at x = 2 is the iterative solution of the equation ( x - 2 )= 0

The graph touches the axis at the intercept and changes direction. The coefficients are quadratic (order 2), so, (x-2)²= (x - 2 )(x - 2)

coefficients are repeated and appears twice. The number of times a given factor appears in the factored form of a polynomial equation is called its multiplicity. Zero associated with this factor, the factor is (x-2), occurs twice, and has a multiplicity of 2 .

thus, the behaviour of graph shows that any point of f(x) which touch or intersect x-axis is call zero of f(x).

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The equation of motion if the mass is initially released from rest from a point 1 foot above the equilibrium position is [tex]\frac{\frac{-sin(8t)}{2} - cos(8t) }{e^{4t} }[/tex] at x = 0, y = -1.

Here, we have been told that the force has a magnitude of = 8 pounds (i)

It stretches a spring to a length of = 1 foot (ii)

The damping force is 0.8 times the instantaneous velocity. (iii)

We use the differential equation of motion of damping force which is =

= mx₂ +λx₁+kx

Using the formula and the values of (i), (ii), and (iii), we get -

= [tex]\frac{\frac{-sin(8t)}{2} - cos(8t) }{e^{4t} }[/tex]

This is the required equation of motion.

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Using p-hat formula and probability,

we get

a) Sampling distribution of p-hat = 0.02029286

b)The probability that in a random sample of 500 adults more than 30% do not own a credit card is

=0.3121

c) The probability that in a random sample of 500 adults between 25% and 30% do not own a credit card is 0.6635

We have given that

29% of adults do not own a credit card according to creditcard.com.

a) Sample size (n) = 500 of adults have own credit card

sample proportion, for the adults do not own a credit= 29% = 0.29

Normal distribution exits here with p

= 1-0.29=0.71 and

Standard error (p-hat) =sqrt(p(1-p)/n)

=sqrt(0.71× 0.29/500)

p-hat = 0.02029286

b) Now, more than 30% do not have own credit card.

P(p-hat>0.3) = P((phat- p)/sqrt(p×(1-p)/n) >(0.3-0.29)/sqrt(0.29× (1-0.29)/500))

=P(Z>0.49) =0.3121 (from standard normal table)

c) Sample size (n) = 500 and p-hat lies between 25% to 30% .

P(0.25<phat<0.3)

= P((0.25-0.29)/sqrt(0.29*(1-0.29)/500) <Z< (0.3-0.29)/sqrt(0.29*(1-0.29)/500))

=P(-1.97<Z<0.49)

=0.6635 (from standard normal table)

Hence, we calculated all the required probabilities.

a) p-hat = 0.02029286

b) P(p-hat>0.3) =0.3121

c) P(0.25<phat<0.3) =0.6635

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Complete question:

According to creditcard.com, 29% of adults do not own a credit card.

a. Suppose a random sample of 500 adults is asked, "Do you own a credit card?" Describe the sampling distribution of p-hat, the proportion of adults who own a credit card.

b. What is the probability that in a random sample of 500 adults more than 30% do not own a credit card?

c. What is the probability that in a random sample of 500 adults between 25% and 30% do not own a credit card?