What is 6.42 written as a fraction in lowest terms?

A) Magnitude of the electric force on charge A is approximately 3.596 × 10⁻² N.

B) Net electric force on charge B will be in the downward direction.

A) To calculate the magnitude of the electric force on charge A, we can use Coulomb's Law:
F = (k * q1 * q2) / r²

where:
- F is the magnitude of the electric force
- k is the electrostatic constant, which is approximately 8.99 × 10⁹ N m²/C²
- q1 and q2 are the magnitudes of the charges (in this case, q1 = 1.0 nC and q2 = 4.0 nC)
- r is the distance between the charges (1 cm, which should be converted to meters: 1 cm = 0.01 m)

Now, plug in the values and solve for F:
F = (8.99 × 10⁹ N m²/C² * 1.0 × 10⁻⁹ C * 4.0 × 10⁻⁹ C) / (0.01 m)²
F ≈ 3.596 × 10⁻² N
The magnitude of the electric force on charge A is approximately 3.596 × 10⁻² N.

B) To determine the direction of the net electric force on charge B, we need to analyze the forces between charge B and charges A and C.

Since both charges A and C are positive and have the same magnitude (1.0 nC), they will both repel charge B. The forces between charges A and B, and B and C will be equal and opposite. Thus, the net electric force on charge B will cancel out horizontally.

However, the vertical component of the force between charge B and charge C will not be canceled out.

Since charge C is positive and has a higher magnitude (4.0 nC) than charge A, it will exert a stronger electric force on charge B. Therefore, the net electric force on charge B will be in the downward direction.

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The scale factor is 10:3

And the value of X=30

A scale factor is defined as the ratio of the scale of a given original object to the scale of a new object that is its representation but of a different size (bigger or smaller). For example, we can increase a rectangle with sides of 2 cm and 4 cm by multiplying each side by an integer, say 2.

Scale factor = new form dimension The basic formula for calculating the scale factor is the dimension of the former shape. The formula for scaling up the original figure is Scale factor = Larger figure dimensions. Figure dimensions are reduced.

From the figure,

Scale factor of AB:AB'

=40:12

=10:3

Therefore, BB':X≅10:3

100/X=10/3

X=(3×100)/10

X=30

Therefore, the scale factor is 10:3

And the value of X=30

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Answer:1

Step-by-step explanation:

Step-by-step explanation:

volume of cube = a ³= 5³= 125 cm³

plz mark my answer as brainlist plzzzz vote me also.

hope this will be helpful to you .

Answer:125

Step-by-step explanation:

Answer:

x-coordinate my dude. the 2nd one is the y.

Step-by-step explanation:

Please mark brainliest!!!

Answer:

∠6 = 125°

Step-by-step explanation:

__________________________________________________________

FACTS TO KNOW :-

When any 2 lines intersect each other at any point , the vertical angles are always equal to each other .

__________________________________________________________

According to the figure ,

∠6 is present vertically opposite to the angle whose measure is 125°.

∴ Hence ∠6 = 125°.

The statement that non-normality of the residuals from a regression can best be detected by looking at the residual plots against the fitted y values is a false statement.

We have a statement and we need to find out if it is true. A negative residual indicates that the model did not fit. This means that the error produced by the model is not the same between variables and observations (that is error is not random). The content is not regular, that is, the content is distributed regularly and we can conclude that the linear model is the appropriate model. If the subject sees a curvilinear pattern such as a U-shaped pattern, we can conclude that a linear pattern is not suitable and a non-linear pattern would be better. These charts are useful for identifying inconsistencies, inconsistencies in error variance, and inconsistencies. Two well-known tests for normality of residues are the Kolmogorov Smirnov test and the Shapiro-Wilk test. So, residual plot can't be used to check the non-normality of the residuals from a regression. Therefore, it is false statement.

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Answer: there is only one number

Answer:

Solo hay un número primo que se puede escribir como suma de dos números primos y también como diferencia de dos números primos.

Espero haber ayudado :D

Expression as a fraction of 0.7 cm³ for 117 mm³ is given by the fraction 0.117 / 0.7.

To write 117 mm³ as a fraction of 0.7 cm³,

we need to convert the units so they match.

Since there are 10 millimeters in a centimeter

1 cm = 10 mm

This implies,

1 cm³ = (10 mm)³

         = 1000 mm³

Now we can express 117 mm³ as a fraction of 0.7 cm³:

117 mm³ / 0.7 cm³

To convert mm³ to cm³, we divide by 1000,

117 mm³ / 1000 = 0.117 cm³

Now we can express it as a fraction,

0.117 cm³ / 0.7 cm³

Simplifying the fraction, we divide the numerator and the denominator by 0.117,

= (0.117 cm³ / 0.117 cm³) / (0.7 cm³ / 0.117 cm³)

= 1 / (0.7 / 0.117)

To divide by a fraction, we multiply by its reciprocal:

= 1 × (0.117 / 0.7)

= 0.117 / 0.7

Therefore, 117 mm³ is equal to the fraction 0.117 / 0.7 when expressed as a fraction of 0.7 cm³.

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To calculate the covariance between the combined claims before and after a surcharge, we need to use the given expectations and variance to find the appropriate values and substitute them into the covariance formula.

To calculate Cov(C, C2), we need to use the following formula:Cov(C, C2) = E(C * C2) - E(C) * E(C2)

First, let's find E(C * C2):

E(C * C2) = E((X + Y) * (X + 1.2 * Y))

Expanding the expression:

E(C * C2) = E(X^2 + 2.2 * XY + 1.2 * Y^2)

Using the given values for E(X^2), E(Y^2), and Var(X + Y), we can calculate E(C * C2):

E(C * C2) = 27.4 + 2.2 * Cov(X, Y) + 1.2 * 51.4

Next, let's find E(C) and E(C2):

E(C) = E(X + Y) = E(X) + E(Y) = 5 + 7 = 12

E(C2) = E(X + 1.2 * Y) = E(X) + 1.2 * E(Y) = 5 + 1.2 * 7 = 13.4

Finally, we can calculate Cov(C, C2):

Cov(C, C2) = E(C * C2) - E(C) * E(C2)

Substituting the values we calculated:

Cov(C, C2) = 27.4 + 2.2 * Cov(X, Y) + 1.2 * 51.4 - 12 * 13.4

Simplifying the expression will give the final result for Cov(C, C2).

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a) The relevant population is the heavy soft-drink users in the given case, and the appropriate sampling design that should be used is  stratified random sampling. The list of all heavy soft-drink users is the sampling frame.

b) Cluster sampling refers to a sampling design where population is divided into naturally occurring groups and a random sample of clusters is chosen.

The advantages are efficient, easy to perform, and used when the population is widely dispersed. The disadvantages are sampling errors, have lower level of precision, and have the standard error of the estimate.

a) The relevant population for the public relations research department to investigate the initial reactions of heavy soft-drink users to a new all-natural soft drink is heavy soft-drink users. The appropriate sampling design that can be used to investigate the issues is stratified random sampling.

Stratified random sampling is a technique of sampling in which the entire population is divided into subgroups (or strata) based on a particular characteristic that the population shares. Then, simple random sampling is done from each stratum. Stratified random sampling is appropriate because it ensures that every member of the population has an equal chance of being selected.

Moreover, it ensures that every subgroup of the population is adequately represented, and reliable estimates can be made concerning the entire population. The list of all heavy soft-drink users can be the sampling frame.

b) Cluster sampling is a type of sampling design in which the population is divided into naturally occurring groups or clusters, and a random sample of clusters is chosen. The elements within each chosen cluster are then sampled.

The advantages of cluster sampling are:

The disadvantages of cluster sampling are:

A situation where cluster sampling would be appropriate is in investigating the effects of a new medication on various groups of people. In this case, the population can be divided into different clinics, and a random sample of clinics can be selected. Then, all patients who meet the inclusion criteria from the selected clinics can be recruited for the study. This way, the study will be less expensive, and it will ensure that the sample is representative of the entire population.

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Answer:

4x^2-13x+4

Step-by-step explanation:

(x^2-5x+6)+(3x^2-8x-2)

Combine like terms

x^2+3x^2-5x-8x+6-2

4x^2-13x+4

Answer:

(might have to round) 1.168224299 euros (I guess round to 1.17)

Step-by-step explanation:

Basically what I did was I made both of the quantities equal to one dollar so £0.8 is a dollar and 100/107 euros is a dollar.

They were both on the same basis so i multiplied by 1.25 to get £1 = 1.168224299 euros

The two most commonly used measures of variability are variance and standard deviation.

1. Variance: Variance measures how spread out a set of data points is from the mean. It calculates the average of the squared differences between each data point and the mean. The formula for variance is sum of squared differences divided by the number of data points.

Example: Let's say we have a set of data points: 2, 4, 6, 8, and 10. The mean of these data points is 6. The differences between each data point and the mean are: -4, -2, 0, 2, and 4. Squaring these differences gives us: 16, 4, 0, 4, and 16. The sum of these squared differences is 40. Dividing this sum by the number of data points (5) gives us a variance of 8.

2. Standard Deviation: Standard deviation is the square root of variance. It measures the average distance between each data point and the mean. Standard deviation is often preferred over variance because it is in the same unit as the data points, making it easier to interpret.

Example: Using the same set of data points as above, the variance is 8. Taking the square root of 8 gives us a standard deviation of approximately 2.83.

In summary, variance measures how spread out the data points are from the mean, while standard deviation gives us a more intuitive understanding of the variability by providing a measure in the same unit as the data points. These measures help us understand how the data is distributed and how much it deviates from the average.

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so hmmm say A(-10 , 5) , B(8 , 2) and the point that partitions them is point C.

\(\textit{internal division of a line segment using ratios} \\\\\\ A(-10,5)\qquad B(8,2)\qquad \qquad \stackrel{\textit{ratio from A to B}}{1:2} \\\\\\ \cfrac{A\underline{C}}{\underline{C} B} = \cfrac{1}{2}\implies \cfrac{A}{B} = \cfrac{1}{2}\implies 2A=1B\implies 2(-10,5)=1(8,2)\)

\((\stackrel{x}{-20}~~,~~ \stackrel{y}{10})=(\stackrel{x}{8}~~,~~ \stackrel{y}{2}) \implies C=\underset{\textit{sum of the ratios}}{\left( \cfrac{\stackrel{\textit{sum of x's}}{-20 +8}}{1+2}~~,~~\cfrac{\stackrel{\textit{sum of y's}}{10 +2}}{1+2} \right)} \\\\\\ C=\left( \cfrac{ -12 }{ 3 }~~,~~\cfrac{ 12}{ 3 } \right)\implies \boxed{C=(-4~~,~~4)}\)

2)  (3, -4)

3) y + 3 + 3/5 (x - 6)

The correct option is b. that there is no preference between the colors.

A null hypothesis is a sort a statistical hypothesis that asserts that there is no statistical significance in a particular set of observations.

Using sample data, hypothesis testing is performed to determine the believably of a theory. It also is written as H0 and is also known to simply as "null."

Some characteristics of null hypothesis are-

So, for this issue, three new colors again for Jeep Grand Cherokee car have been proposed. Its null hypothesis that there is no difference between the colors, that are silvered-blue, almond, and willow green.

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The complete question is-

Three new colors have been proposed for the jeep grand cherokee vehicle. they are silvered-blue, almond, and willow green. the null hypothesis for a goodness-of-fit test would be

a. willow green is preferred over the other colors.

b. that there is no preference between the colors.

c. any one color is preferred over the other colors.

d. impossible to determine.

An equivalent form of the index 8.723 x 10-¹⁰ is 0. 0000000008723

The index form of a number is simply that number written as an exponential expression, or even as a single number that is raised to another number.

Index form is also known as standard form

Given the index form;

⇒ 8.723 x 10-¹⁰

⇒ 8. 723 × 10^ -(10)

This means that there 10 zero digits from the left end of the given decimal, it is expressed as;

0. 0000000008723

Thus, an equivalent form of the index 8.723 x 10-¹⁰ is 0. 0000000008723

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Answer:

A"(-1, -3), B"(-2, -6), C"(1,-7)

Step-by-step explanation:

y= -4 is a horizontal line that cuts y-axis at (0, -4)

A'(-4, -5), B'(-5,-2), C'(-2,-1) are given on thhe graph

first we reflect over the line m, y= -4

A"(-4, -3), B"(-5, -6), C"(-2,-7) because the line m is the bisector of what conects the image and preimage points

second we translate T(3,0) so you add a 3 to the x coordinate of each point

A"(-4+3, -3), B"(-5+3, -6), C"(-2+3,-7)

A"(-1, -3), B"(-2, -6), C"(1,-7)

Given:

A four member bowling team decided they wanted new outfits. Shirts cost $15 each, pants cost $26 each and shoes cost $40 each.

Required:

We need to find the total cost.

Explanation:

First we find total cost for 1 member

$81 for each member but here we have 4 members so we need to multiply with 4 to the each person's cost

Final answer:

Cost for 1 member is $81

cost for all member is $324

Answer: $324

Explanation: Alright, let's pretend that you are the cost manager or fiduciary (a person who holds assets in trust for someone else. That person has a fiduciary duty to take care of the money.)
First thing is, we need to find the cost for a single member of the team. Now ofcourse each person needs atleast one shirt, pants and one pair of shoes. How much would a shirt, pant and a pair of shoes cost ? Calculate:
one shirt  - - -  $15
one pant  - - - $26
1pair shoe - - +$40
Total bills:       $81

Each member needs atleast $81. There are four members in total. Thus if one member needs 81 dollars then 4 members would need $81 + $81 + $81 + $81 = $324  OR   for shortcut method: $81 * 4 = $324

Done! That's all. Hope it helped

Answer:

0.012

Step-by-step explanation:

0.6/48.24

1. multiply numerator and denominator by 100 to get 60/4824

2. divide 60 by 4824

3. you get 0.012

( i would've written out how to get that answer but there are about 10 steps and it's really hard to type them out)

Answer

Explanation

The perimeter of a figure

The slope of a line perpendicular to the line passing through the points (0,4) and (-3,0) is -3/4.

To find the slope of a line perpendicular to a given line, we need to take the negative reciprocal of the slope of the given line.

Given the points (0,4) and (-3,0), we can calculate the slope of the given line using the slope formula:

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

Let's substitute the values:

slope = (0 - 4) / (-3 - 0)

= -4 / -3

= 4/3

The slope of the given line is 4/3.

To find the slope of a line perpendicular to this line, we take the negative reciprocal of 4/3:

slope of perpendicular line = -1 / (4/3)

= -1 * (3/4)

= -3/4

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Probability that the mean diamter of the sample shaftes would differ from the population mean by less than 0.1 inches is 0.4778.

What do you mean by standard deviation?

The standard deviation is a statistical indicator of how widely distributed a set of values are. A random variable, sample, statistical population, data set, or probability distribution's standard deviation is equal to the square root of its variance.

Here, it is given that

Standard deviation , σ = 1.3

Mean diamter, μ = 202

Number of shafts , n = 70

σ\(_{x}\) = σ/\(\sqrt{n}\) = 1.3/\(\sqrt{70}\) = 0.1554

Difference less than 0.1 = 202 - 0.1 = 201.9 , 202 + 0.1 = 202.1

P(\(\overline{x}\) < 0.1) = P(201.9 < x < 202.1)

P ( 201.9 - 202 /  0.1554 ) < \(( \bar x - \mu\bar x /\sigma\bar x)\) < ( 202.1 - 202 /  0.1554 )

P ( - 0.1 / 0.1554 < z < 0.1 /  0.1554 )

P (-0.64 < z < 0.64 )

P ( z < 0.64) - p ( z < -0.64 )

Using z table

= 0.7389 - 0.2611

= 0.4778

Probability =0.4778

Therefore, Probability that the mean diamter of the sample shaftes would differ from the population mean by less than 0.1 inches is 0.4778.

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Answer:

c) f = 28

Step-by-step explanation:

Given problem,

→ f³ = 21952

Now the value of f will be,

→ f³ = 21952

→ f = ³√21952

→ [ f = 28 ]

Let's check the following,

→ 28³

→ (28 × 28) × 28

→ 784 × 28 = 21952

Hence, option (c) is correct.

Answer:

add multiply divide or subtract make sure to use Pemdas then and you should have your answer

Step-by-step explanation:

Answer:

r = 10

Step-by-step explanation:

The equation of a circle centred at the origin is

x² + y² = r² ( r is the radius )

x² + y² = 100 ← is a circle centred at the origin with

r² = 100 ( take the square root of both sides )

r = \(\sqrt{100}\) = 10

Answer:

2x

Step-by-step explanation:

let, \(\tt f(x) = a^2+x^2\)

Differentiating both side with respect to x.

\(\tt \frac{d}{dx}f(x) = \frac{d}{dx}(a^2+x^2)\)

Using sum/difference rule

\(\tt \frac{d}{dx}f(x) = \frac{d}{dx}(a^2) + \frac{d}{dx}(x^2)\)

Now, using Power rule of derivative :  \(\boxed{\tt x^n=nx^{(n-1)}}\) .

\(\tt f'(x)=0+2x^{2-1}\)

\(\tt f'(x}=0+2x\)

\(\tt f'(x)= 2x\)

Therefore, the derivative of  \(\tt a^2+x^2\) is 2x.

Note: derivative of constant term is 0. here a^2 is constant.

Explanation

We are given the following:

We are required to determine the surface area of a cylinder. This can be achieved by using the formula:

Hence, the answer is 301.44m².

Answer:

Step-by-step explanation:

A