Please help me with this question.

The frequency distribution table is given as

Length (in)                      Frequency

2.720  - 2.729                         1

2.730  - 2.739                          5

2.740  - 2.749                          9

2.750 - 2.759                         13

2.760  - 2.769                         2

Given that the sample of the 30 screw lengths

2.753 2.762 2.752 2.735 2.733 2.747 2.751 2.723 2.754 2.751 2.754 2,742 2.748 2.737 2.751 2.752 2.764 2,744 2.744 2,748 2.741 2.762 2.758 2.756 2.747 2.736 2.752 2.736 2.759 2.746

For constructing a frequency distribution :

Lower class limit = 2.720​ in.

Class width = 0.010 in

Frequency Distribution  Table :

Length (in)                      Frequency

2.720  - 2.729                         1

2.730  - 2.739                          5

2.740  - 2.749                          9

2.750 - 2.759                         13

2.760  - 2.769                         2

Total                                        30

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The perimeter of the rectangle is (6x - 2)ft and the area of the rectangle is (2x^2 - 5x - 12) square ft.

What is a rectangle?

A rectangle is a sort of quadrilateral with parallel sides that are equal to one another and four vertices that are all 90 degrees apart. Because of this, it is also known as an equiangular quadrilateral.

We are given that the length of a rectangle is (2x + 3) ft. and the width is

(x - 4) ft.

We know that perimeter of rectangle = 2(Length + Width)

So,

⇒Perimeter = 2(2x + 3 + x - 4)

⇒Perimeter = 2(3x - 1)

⇒Perimeter = (6x - 2)ft

We know that area of rectangle = Length * Width

So,

⇒Area = (2x + 3) * (x - 4)

⇒Area = 2x^2 - 8x + 3x - 12

⇒Area = (2x^2 - 5x - 12) square ft

Hence, the perimeter of the rectangle is (6x - 2)ft and the area of the rectangle is (2x^2 - 5x - 12) square ft.

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The Sun's diameter is 1.075*10²  times the Earth's diameter.

Sun's Dimensions.The Sun's diameter is equal to 1.4 x 106 km when we multiply its distance by its observed angular diameter (about 0.5 degrees).

This is around ten times as big as Jupiter, the largest planet, and about 100 times as big as the Earth.

The Sun's diameter is times the Earth's diameter.  

We are given the following in the question:

Sun's diameter = 860,000 miles

Earth's diameter = 8000 miles

Comparison of Sun's and Earth's diameter:

sun s diameter / earth diameter

=  860000/8000

8.6 *10(5)/8*10(3)

= 1.075*10(2)

Thus, the Sun's diameter is 1.075*10²  times the Earth's diameter.

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Answer:

Step-by-step explanation:

b= -3

Answer:

Equation = (6*3) - 2

Solution

Let x represent the unknown number

The number is multiplied by 6

= (6 × x )

= 6x

two is subtracted from the product

= 6x - 2

The product is equated to 3

= 6x-2= 3

Hence the equation is 6x-2= 3

The output column, S, of the given input-output table was created from the student ID 21444368 using an algorithm where if the student ID digit is an even integer, a 0 is placed in the corresponding row of column S, and if the student ID digit is an odd integer, a 1 is placed in the corresponding row of column S.

Student ID: 81725225

P Q R S

1 1 1 0

1 1 0 1

1 0 1 1

0 1 0 0

0 0 1 1

0 1 1 0

0 0 0 1

Student ID: 81725225

P: The first digit of my student ID is 8 so it is an even integer, therefore I place a 0 in row 1 of column P.

Q: The second digit of my student ID is 1 so it is an odd integer, therefore I place a 1 in row 2 of column Q.

R: The third digit of my student ID is 7 so it is an odd integer, therefore I place a 1 in row 3 of column R.

S: The fourth digit of my student ID is 2 so it is an even integer, therefore I place a 0 in row 4 of column S.

The resulting table is:

P Q R S

1 1 1 0

1 1 0 1

1 0 1 1

0 1 0 0

0 0 1 1

0 1 1 0

0 0 0 1

The output column, S, of the given input-output table was created from the student ID 21444368 using an algorithm where if the student ID digit is an even integer, a 0 is placed in the corresponding row of column S, and if the student ID digit is an odd integer, a 1 is placed in the corresponding row of column S. The same algorithm was applied to my student ID 81725225, resulting in the table shown above.

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   The amount that should be recorded for the asset purchase is $375,000. This is the amount of the loan that is being used to purchase the asset.

   The amount that should be recorded for the liability used to purchase the asset is also $375,000. This is the amount of the loan that is being taken on to purchase the asset.

The factor of the expression could be [tex](x + 1)(x + 2)((x^2 -x + 1)[/tex]

Factorization is expressing a mathematical quantity in terms of multiples of smaller units of similar quantities.

factorization is the method of breaking a number into smaller numbers that multiplied together will give that original form.

We are given a expression as;

[tex]x^4 + 2x^3 + x + 2[/tex]

Thus,

[tex](x^4 + 2x^3) + (x + 2)[/tex]

Factor out x^3

[tex]x^3(x + 2) + (x + 2)[/tex]

Then;

[tex](x^3 + 1)(x + 2)[/tex]

Therefore, the factor of the given expression is;

[tex](x + 1)(x + 2)(x^2 -x + 1)[/tex]

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The answer is X=165 lbs (or) 74.84 kg.

Solution:

Given,

1kg/2.2lbs = X/165lbs,

So we get 1kg×165lbs= 2.2lbs×X,

By converting kg to lbs ∵ 1 kg= 2.2 lbs,

X=165 lbs.

∴ Hence X=165 lbs

The coordinates (4.0 , 4.5) to the center is not the distance of radius

From the circle formula centered at origin: x² + y² = r²

Where r is the radius of the circle. and by substitution for the various values of x, y and r we have

x² + y² = 6² = 36

Also, substituting the values of the lengths of the line we have

(4)² + (4.5)² = 16 + 20.25 = 36.25 ≠ 36

This proves the diagonals of the rhombus ABCD bisect each other

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The expression that is equivalent to (16x^4)^1/2 is (64x^6)1/3.

Equivalent expressions are expressions that accomplish the same thing even when they have distinct appearances. Two algebraic expressions that are equivalent share a similar value whenever we enter exact same thing for the variable.

Given that;

[tex](16x^4)^{\frac{1}{2}}[/tex]

[tex]=\sqrt{16x^4}[/tex]

= 4x²

From the given options, (64x^6)^1/3 verifies the identity and shows that it is equivalent to (16x^4)^1/2.

[tex](16x^4)^{\frac{1}{2}} = (64x^6)^{\frac{1}{3}}[/tex]

[tex](16x^4)^{\frac{1}{2}} = (4^3)^{\frac{1}{3}} (x^6)^{\frac{1}{3}}[/tex]

[tex]4x^2= (4) (x^6)^{\frac{1}{3}}[/tex]

[tex]4x^2=4x^2[/tex]

Therefore, we can conclude that the expression that is equivalent to (16x^4)^1/2 is (64x^6)1/3

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Answer: Oh well how you doing?

Step-by-step explanation:

If needed call prevention hotline... if you know what I mean

Answer:

that’s brazy

Step-by-step explanation:

Between 105.9 and 309.3 pounds, Chebyshev's Theorem guarantee that we will find at least 95% of the patients.

k = 4.5.

Weight 4.5 standard deviations below the mean is 207.6 − 4.5 (22.6) = 105.9 pounds.

Weight 4.5 standard deviations above the mean is 207.6 + 4.5 (22.6) = 309.3 pounds.

Therefore, at least 95% of patients weigh between 105.9 and 309.3 pounds.

In probability theory, the Chebyshev inequality guarantees that for any sample data or probability distribution, nearly all values are close to the mean. Precisely, that no more 1/k2 of the distribution value exceeds the k standard deviation.

Chebyshev's inequality theorem can be used to find the probability range for an unknown distribution based on its mean and variance.

Chebyshev is named after a Russian mathematician, although the first formulation of the inequality was obtained from his colleague, Irénée-Jules Bienaymé. Chebyshev's inequality theorem was introduced without any proof in 1874, which later, in 1884,

Chebyshev's student, Andrey Markov presented a proof. Therefore, in the context of the analysis, the Chebyshev inequality is also expressed in the Markov inequality.

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The compound inequality for the graph shown above include the following:

x < -2.

x > 5.

In Mathematics, a number line can be defined as a type of graph with a graduated straight line which comprises both positive and negative numerical values that are placed at equal intervals along its length.

Since the first point is at -2 and the arrow points to the left of the number line, it represents the less than (<) inequality symbol and should be written as x < -2.

Additionally, the second point is at 5 and the arrow points to the right of the number line, it represents the greater than (>) inequality symbol and should be written as x > 5.

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Answer:

below

Step-by-step explanation:

This is the same as    (-1)(-2y-4u+2)   = 2y + 4u - 2

The year the population of that city was 290,000 is 1988.

A model function is a mathematical or computational representation of a system or process that is designed to capture its behavior, relationships, and interactions.

The model is p(x) = 80,000 ∛(x - 1940)

Now use p(x) = 290,000and solve for x

290,000 = 80,000 ∛(x - 1940) =

290,000 / 80,000 = ∛(x - 1940)

29/8 = ∛(x - 1940)

x - 1940 = [29/8]³

x - 1940 = 47.63

x = 1940 +  47.63

x = 1987.63

Therefore, the year is 1988

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British sterling silver =    321.1   grams

Copper =  8.9   grams

========================================================

Work Shown:

The two amounts add to 330 grams total. The x is some number in the interval 0 < x < 330.

We want to end up with 330 grams of 10% copper, so we want 0.10*330 = 33 grams of pure copper after mixing the two metals.

Set the 33 equal to the expression -0.925x+330 and solve for x.

-----------

-0.925x+330 = 33

-0.925x = 33-330

-0.925x = -297

x = -297/(-0.925)

x = 321.081 approximately

x = 321.1 when rounding to one decimal place

330-x = 330-321.1 = 8.9

-----------

We'll need  321.1   grams of British sterling silver.

We'll also need  8.9   grams of pure copper.

Set A is a subset of set B if every element of A is also an element of B

If every element of set A is also an element of set B, then set A is a subset of set B. This is expressed in symbols as A B or. For example, suppose you’re representing all of the nations in the globe, and set A represents Finland and Greece, while set B represents all of Europe.

If a set A is a subset of a larger set B, the circle representing set A is drawn within the circle representing set B.

If sets A and B share certain components, we can symbolize them by drawing two overlapping circles.

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For the given number line plot the inequality obtained is { -∞ < x < -2 and 5 < x < ∞}.

What is an inequality?

In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.

To represent inequalities on a number line show the range of numbers by drawing a straight line and indicating the end points with either an open circle or a closed circle.  

An open circle shows it does not include the value.

A closed circle shows it does include the value.

Let the unknown value be x.

The first range is starting form -2 and moving towards -∞.

Since the circle is open it will not include the value.

So the inequality is -∞ < x < -2.

The second range is starting form 5 and moving towards ∞.

Since the circle is open it will not include the value.

So the inequality is 5 < x < ∞.

Therefore, the inequality is { -∞ < x < -2 and 5 < x < ∞}.

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The length of the side BC is 96 units.

A triangle is a two dimensional figure which consist of three vertices, three edges and three angles.

Sum of the interior angles of a triangle is 180 degrees.

Given that AD is an altitude of triangle ABC.

Altitude of a triangle is the line of perpendicular drawn from a vertex to the opposite side.

∠ADC = ∠ADB = 90°

Given that, ∠ADC = 4x + 10

4x + 10 = 90

4x = 80

x = 20

Length of BC = BD + DC

                      = 2x + 3x - 4

                      = 5x - 4

                      = (5 × 20) - 4

                      = 100 - 4

                      = 96

Hence the length of the side BC is 96.

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A) The probability that you will join them is 0.523;

B)  If you end up joining them, the probability your friends have decided to visit a national park is 0.50.

Note that probability is an area of mathematics that deals with numerical representations of how probable an event is to occur or how likely a statement is to be true. The probability of an occurrence is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.

In the above case, Note that to determine the probability that you will join them, we need to use the formula for conditional probability, which is:

P(A and B) = P(A|B) * P(B)

In this case, A is the event that you join them, and B is the event of your friends deciding to visit either a national park or a city in the USA.

Given the above, we have:

P(join and national park) = P(join|national park) * P(national park) = 0.75 * 0.35

P(join and city) = P(join|city) * P(city) = 0.40 * 0.65

Thus to obtain the probability that you will join them: we must add the two probabilities: P(join and national park) and P(join and city)

⇒ P(join) = P(join and national park) + P(join and city)

= 0.75 * 0.35 + 0.40 * 0.65

= 0.523

Thus, it is correct to state that the probability or likelihood that you join them is: 0.523

B) If you decide to join them, the probability that your friends have decided to go to a national park is determined using the Bayes Theorem.  This theorem is given as:

P(B|A) = P(A|B) * P(B) / P(A)

Where A is the event of you going with them, and B is the event of your friends deciding to go to a national park.

P(national park|join) = P(join|national park) * P(national park) / P(join)

= 0.75 * 0.35 / 0.525

= 0.5019120459
[tex]\approx[/tex] 0.50

Thus, it is correct to state that the probability your friends have decided to visit a national park is 0.57 if you eventually join them.

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A=1/2bh and b=2A/h so

b=2A/h =2(12cm^2)/3cm=8cm

In order to find the base

We apply the area of a triangle formula to find the base

We know the formula to find the area of a triangle is,

[tex]A =\frac{1}{2}XbXh[/tex]

Here the area and the height is given

So the base is

[tex]12 = \frac{1}{2} X bX3[/tex]

Substituting the values we get

[tex]\frac{12X2}{3} = b[/tex]

[tex]8cm = b[/tex]

If 1 gallon = 4.546 litres, then 10 litres in gallon is approximately 2.2 gallons.

1 gallon = 4.546 litres,

∴ 1 litre = [tex]\frac{1}{4.546}[/tex] = 0.2199 gallon

∴ 10 litres = 10 × 0.2199 = 2.199 gallons ≅ 2.2 gallons

Thus, 10 litres in gallon is approximately equal to 2.2 gallons.

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The actual interval of existence for the solution is all real numbers, including t = 0.

a. The characteristic equation for the differential equation is

2t dy/dt = 8y,

which gives us

dy/dt = 4/t y.

Separating variables, we have

dy/y = 4/t dt,

which integrates to

ln|y| = 4 ln|t| + C,

where C is an arbitrary constant of integration.

Taking the exponential of both sides, we obtain

|y| = Ce^(4ln|t|),

which gives us

y = C t^4.

Using the initial condition y(-1) = 2, we can find the value of C:

y(-1) = C(-1)^4

2 = C(-1)^4

C = -2.

So the solution to the initial value problem is

y(t) = -2 t^4.

b. The largest interval of the form a < t < b on which the existence and uniqueness theorem for first order linear differential equations guarantees the existence of a unique solution is t ≠ 0, since the coefficient of the differential equation is undefined at t = 0.

c. The actual interval of existence for the solution is all real numbers, including t = 0.

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Answer:

To find out how many milligrams more need to be added to bring the total weight of the supplies to 10,000 mg, we can subtract the current weight from 10,000:

10,000 - 3.69 g = 10,000 - 3,690 mg

Answer:

6,310 mg more need to be added to bring the total weight of the supplies to 10,000 mg.

a) The percentage of test takers that scored 1420 or higher is of: 2.87%.

b) The percentage of test takers that scored 800 or lower is of: 10.03%.

c) The percentage of students between 1500 and 1600 is given as follows: 0.8%.

d) The number of students eligible for the honors program is given as follows: 1040 students.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation for this problem are given as follows:

[tex]\mu = 1050, \sigma = 195[/tex]

The proportion of scores of 1420 or higher is one subtracted by the p-value of Z when X = 1420, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (1420 - 1050)/195

Z = 1.9

Z = 1.9 has a p-value of 0.9713.

1 - 0.9713 = 0.0287 = 2.87%.

The proportion of test takers that scored 800 or lower is the p-value of  Z when X = 800, hence:

Z = (800 - 1050)/195

Z = -1.28.

Z = -1.28 has a p-value of 0.1003.

The proportion between 1500 and 1600 is the p-value of Z when X = 1600 subtracted by the p-value of Z when X = 1500, hence:

Z = (1600 - 1050)/195

Z = 2.82

Z = 2.82 has a p-value of 0.9976.

Z = (1500 - 1050)/195

Z = 2.31

Z = 2.31 has a p-value of 0.9896.

Hence:

0.9976 - 0.9896 = 0.008 = 0.8%.

The proportion above 1550 is one subtracted by the p-value of Z when X = 1550, hence:

Z = (1550 - 1050)/195

Z = 2.56

Z = 2.56 has a p-value of 0.9948.

Hence:

1 - 0.9948 = 0.0052.

Out of 200,000 students, the number is given as follows:

0.0052 x 200,000 = 1040 students.

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The price of one currency in respect to another is referred to as its exchange rate.

An exchange rate in the world of finance is the price at which one currency will be exchanged for another. The majority of the time, currencies are national ones, but they can also be supra-national ones like the euro or sub-national ones like Hong Kong.

A currency's price in relation to another is known as its exchange rate. You can have fixed or fluctuating exchange rates. While a country's central bank controls fixed exchange rates, the process of supply and demand on the open market controls floating exchange rates.

The rate at which one currency can be exchanged for another between countries or economic zones is known as the exchange rate. It is crucial in assessing trade and capital movement dynamics and is used to calculate the value of various currencies in respect to one another.

Convert the currency:

£ 400 × R 19.29/£2 = R 7,716

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Answer:

Step-by-step explanation:

x-2=-9

Add 2 on both sides

x=-7

Answer:

[tex]x=11[/tex]

Step-by-step explanation:

x−2=9

Add 2 to both sides.

x=9+2

Add 9 and 2 to get 11.

x=11

pls tell me if wrong