Do the values in the table represent a proportional relationship?

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.

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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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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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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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 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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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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Answer:

Step-by-step explanation:

The ratio of cocoa powder to one cup of milk is 1/4 cup of cocoa powder to 3 3/4 cups of milk or 1/4 : 3 3/4 or 1 : 15.

The required solution of the equation is -16.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign. Equation, statement of equality between two expressions consisting of variables and/or numbers.

Given :six more than the quotient of a number and 8 is equal to 4

To solve this, we can convert the statement into an algebraic equation, Express it in an equation:

6+(x/8) = 4

subtracted 6 from both sides,

x/8 = -2

multiplied both sides by 8,

x = -16

Therefore, the required solution of the equation is -16.

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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 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 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

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

In a sample of size 100, the median splits the data into two equal parts of 50 observations each. So, 50 observations are below the median and 50 observations are above the median.

The first quartile (Q1) separates the lowest 25% of the data from the rest, so 50 observations are between the median and Q1.

The interquartile range (IQR) is defined as the difference between the third quartile (Q3) and Q1, and represents the range of the middle 50% of the data. Since the IQR contains both Q1 and the median, it encompasses all observations between Q1 and the median,

or a total of 75 observations.

therefore the answer is 25,50,75

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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 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 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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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:

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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Answer:

Step-by-step explanation:

b= -3

Answer:

Let x be the amount of alloy 1 used, and y be the amount of alloy 2 used.

We know that:

x + y = 53 (total weight of alloy 3 is 53 pounds)

0.35x + 0.69y = 0.40(53) (40% of the alloy 3 is titanium)

We can use the first equation to solve for one of the variables in terms of the other:

y = 53 - x

Substitute this expression into the second equation:

0.35x + 0.69(53-x) = 0.40(53)

0.35x + 36.97 - 0.69x = 21.2

-0.34x = -15.77

x = 46.44 pounds of alloy 1.

y = 53 - x = 6.56 pounds of alloy 2.

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.

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 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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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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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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Given:-

[tex] \: [/tex]

[tex] \: [/tex]

To find:-

[tex] \: [/tex]

[tex] \: [/tex]

Solution:-

[tex] \: [/tex]

[tex] \: [/tex]

now , put the value of x= -3 in given eqⁿ ∼

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

hope it helps! :)