what is 18/42 in simpist form?

Answer:

Step-by-step explanation:

Look at the picture.

Answer:

Step-by-step explanation:

Sorry I can't explain how it is done. It is very difficult to explain on paper.

Answer

D. WY = 12, m angle XWZ = 51°

Step-by-step explanation:

since WX is 6 and XY is congruent to WX they are both 6 so add them together and you get 12 for WY

6+6=12

because we need to find the missing angle we know that we have 2 other angles, 39°, and our right angle that is 90° so we subtract both of these angles from 180

180-90-39=51°

Hope this helped

Answer:

\(t = 0.375s\)

Step-by-step explanation:

Given

\(h(t) = -16t^2 + 4t + 33\) --- driver 1

\(Rate = 2ft/s\) -- driver 2

\(height = 33ft\)

Required

The time they passed each other

First, we determine the function of driver 2.

We have that:

\(Rate = 2ft/s\) and \(height = 33ft\)

So, the function is:

\(h_2(t) = Height - Rate * t\)

\(h_2(t) = 33 - 2t\)

The time they drive pass each other is calculated as:

\(h(t) = h_2(t)\)

\(-16t^2 + 4t + 33= 33 - 2t\)

Collect like terms

\(-16t^2 + 4t + 2t= 33 - 33\)

\(-16t^2 + 6t= 0\)

Divide through by 2t

\(-8t + 3= 0\)

Solve for -8t

\(-8t = -3\)

Solve for t

\(t = \frac{-3}{-8}\)

\(t = 0.375s\)

Statistics computed for larger random samples tend to be less variable compared to statistics computed for smaller random samples.

This statement is based on the concept of the Central Limit Theorem (CLT) in statistics. According to the CLT, as the sample size increases, the distribution of the sample mean approaches a normal distribution regardless of the shape of the population distribution. This means that the variability of the sample mean decreases as the sample size increases.

The variability of a statistic is commonly measured by its standard deviation or variance. When working with larger random samples, the individual observations have less impact on the overall variability of the statistic. As more data points are included in the sample, the effects of outliers or extreme values tend to diminish, resulting in a more stable and less variable estimate.

In practical terms, this implies that estimates or conclusions based on larger random samples are generally considered more reliable and accurate. Researchers and statisticians often strive to obtain larger sample sizes to reduce the variability of their results and increase the precision of their statistical inferences.

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Step-by-step explanation and Answer

Since the interest rate is 5%, and the first loan was borrowed on May 1, we can calculate the interest on the first loan by using the formula:

Interest = Principal x Rate x Time

In this case, the principal is 2000, the rate is 5% (expressed as a decimal), and the time is (September 24 - May 1) = 4.5 months

So, Interest = 2000 x 0.05 x 4.5/12 = 50

The same applies to the second loan of 1000, so the interest on this loan is:

Interest = 1000 x 0.05 x (4.5/12) = 25

To find the total amount returned, we add the interest on both loans to the total principal borrowed:

total = 2000 + 1000 + 50 + 25 = 3075

Therefore, the total amount returned is Ks 3075

Answer:

1.28 m

Step-by-step explanation:

48/30 = x/.8

cross multiply

30x = 48(.8)

30x = 38.4

x = 38.4/30

x = 1.28 m

Answer:

6^7 (last choice)

Step-by-step explanation:

6^3 x 6^4 ---> product of exponent law

keep the base the same (only works if the base are the same)

add the exponents

^3 + ^4 = ^7

put the base back

6^7

The quotient of the provided polynomial divide by the (x+6) with the help of synthetic division method is,

\(f(x)=4x^2-27x+167-\dfrac{996}{x+6}\)

The factor of a polynomial is the terms in linear form, which are when multiplied together, give the original polynomial equation as result.

The polynomial given in the problem is,

\(4x^3-3x^2+5x+6\)

This polynomial is divided by the linear factor (x+6). Thus use -6 to for the synthetic division of polynomial as,

-6    | 4    -3        +5         6

x            -24     +162    -1002

Add the numbers as,

          4   -27   167   -996

Put these values, we get,

\(f(x)=4x^2-27x+167-\dfrac{996}{x+6}\)

Hence, the quotient of the provided polynomial divide by the (x+6) with the help of synthetic division method is,

\(f(x)=4x^2-27x+167-\dfrac{996}{x+6}\)

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Answer: D

Step-by-step explanation:

Edge 2023

Answer:

510

Step-by-step explanation:

(0.68)750

shift decimal places

510.00

refine:510

We will see that the total number of ways in which we can distribute 20 different prizes among 180 people is:

C =  6.818e46

Here we need to count how many selections do we have. Each prize will be a selection, so we have 20 selections.

Now we need to count the numbers of 6for each selection.

For the first prize, there are 180 options.

For the second prize, there are 179 options (because one person already got a prize).

For the third prize, there are 178 options.

And so on.

The total number of combinations is given by the product between the numbers of options:

C = 180*179*178*...*161*160 = 6.818e46

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Work done can be defined simply as the force times distance covered.

To find work, use the equation:

Work = Force x distance

Force is in Newtons

Distance is in meters

The unit of work is Joule.

Another method to find work is:

W = F cos θ⋅ d

F = force

d = displacement

Here, the force is extended to the direction of motion at angle θ.

The ratio of the cooling time of Earth to the cooling time of the exoplanet is 16,777,216.

An exoplanet, also known as an extrasolar planet, is a planet that orbits a star other than the Sun, which is part of our solar system. An exoplanet is one of many planets that might exist in the universe outside of our solar system.

The ratio of the cooling time of Earth to the cooling time of the exoplanet can be determined using Stefan-Boltzmann's Law and Wien's Law.

We first need to use the Stefan-Boltzmann Law in order to calculate the cooling time.

σT⁴ = L/(16πR²)

σ(5780)⁴ = (3.846 × 10²⁶ W)/(16π(6.3781 × 10⁶)² m²)

Ratio of the exoplanet's radius to the Earth's radius:

re/rE = 8.00

Ratio of the exoplanet's mass to the Earth's mass:

me/mE = (re/re)³ = 8³ = 512 (since density is assumed to be the same for both planets)

Ratio of the exoplanet's luminosity to the Earth's luminosity:

Le/LE = (me/mE)(re/rE)² = 512(8)² = 32768

Ratio of the exoplanet's temperature to the Earth's temperature:

Te/TE = (Le/LE)¹∕⁴ = 32768¹∕⁴ = 32.0

The Wien Law can now be used to determine the ratio of the cooling times of the two planets.

(T/wavelength max)E = 2.898 × 10⁻³ m K(5780 K) = 1.68 × 10⁻⁸ m (using Earth as the comparison planet)

(T/wavelength max)e = 2.898 × 10⁻³ m K(Te)(8.00) = wavelength max (using the exoplanet)

Ratio of the wavelengths:

wavelength max,e/wavelength max,E = (Te/TE)(re/rE) = 32.0 × 8.00 = 256

Ratio of the cooling times:

cooling time,e/cooling time,E = (wavelength max,e/wavelength max,E)³ = 256³ = 16,777,216

Hence, the ratio of Earth's cooling time to the exoplanet's cooling time is 16,777,216.

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Step-by-step explanation:

there is no big "trick" involved.

you just need to do the multiplication and then move the terms into the right spot, so that the x-, y- and constant terms are in the same place as the generic Ax + By = C

y + 5 = 4(x + 1)

y + 5 = 4x + 4

-4x + y = -1

or (after multiplying both sides by -1)

4x - y = 1

yes, B = 1 (or -1), so you could write 1y (or -1y) instead of only y (or -y).

but nobody does that.

Answer:

D

Step-by-step explanation:

The line with points greater than +2 are the solution to the given inequality.

inequality : An inequality is used to make unequal comparisons between two expressions or numbers.

expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.

equation : A mathematical equation is used to equate two expressions.

Given is the inequality -

11x + 14 < - 8

The given inequality is -

11x + 14 < - 8

11x < - 8 - 14

11x < - 22

x < - 2

x > 2

Therefore, the line with points greater than +2 are the solution to the given inequality.

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The missing length in the given triangles CG is 18.

A triangle is a three-sided polygon that consists of three edges and three vertices.

The given triangles ABC and CFG are similar triangles.

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .

AC/CG=BC/CF

66/CG=154/42

66×42=154CG

2772=154 CG

Divide both sides by 154

CG=18

Hence, the missing length in the given triangles CG is 18.

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Answer:

this is the answer (-3,-6)

True, there exists a linear transformation T: V → W such that T(x1) = y1 and T(x2) = y2.

A linear transformation is a function that maps vectors from one vector space to another in a linear manner. In this case, we are given two vectors x1 and x2 belonging to vector space V, and two vectors y1 and y2 belonging to vector space W.

According to the given statement, we need to determine if there exists a linear transformation T that maps x1 to y1 and x2 to y2. Since x1 and x2 belong to V and y1 and y2 belong to W, we can say that the vectors are compatible for a linear transformation from V to W.

By definition of a linear transformation, T(x1) = y1 and T(x2) = y2, which means that the linear transformation T maps x1 to y1 and x2 to y2, respectively. This implies that there exists a linear transformation T: V → W that satisfies the given conditions.

Therefore, the answer is true.

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Step-by-step explanation:

The coefficient of C in the inequality 56C+64R<9000 represents the rate of fuel consumption while flying through clear skies. From the inequality, we can see that the rate of fuel consumption while flying through clear skies is 56 gallons per minute.

To find the initial fuel capacity of the airplane, we need to set the values of C and R to zero in the inequality 56C+64R<9000, since this represents the scenario where the plane flies entirely through clear skies and does not encounter any rain clouds.

56(0) + 64(0) < 9000

Simplifying the inequality, we get:

0 < 9000

This means that the inequality is true for any positive value of C and R, including C = 0 and R = 0. Therefore, the airplane has more than 0 gallons of fuel before takeoff, but the exact amount is not specified in the given information.

The given inequality is:

56C + 64R < 9000

We know that the airplane consumes fuel at a constant rate while flying through clear skies. Let the fuel consumption rate be F (in gallons per minute) and let the amount of fuel the airplane has before takeoff be T (in gallons).

We need to find the values of F and T that satisfy the given inequality.

First, we can simplify the inequality by dividing both sides by 8:

7C + 8R < 1125

Next, we can use the fact that the airplane consumes fuel at a rate of 64 gallons per minute while flying through rain clouds to write an expression for the total fuel consumption during R minutes:

64R

Similarly, the total fuel consumption during C minutes while flying through clear skies is:

FC

The total fuel consumption during both C and R minutes can be expressed as:

FC + 64R

We know that the total fuel consumption must be less than the initial amount of fuel, which is T. Therefore, we can write:

FC + 64R < T

Substituting FC = F * C, we get:

F * C + 64R < T

We can rearrange this inequality to solve for T:

T > F * C + 64R

Now we can use the inequality 7C + 8R < 1125 to solve for F and T.

Let's assume the airplane has enough fuel to fly for 1 hour (60 minutes) in clear skies and no rain clouds. Then C = 60 and R = 0. Substituting these values into the inequality, we get:

56(60) + 64(0) < 9000

3360 < 9000

This is true, so our assumption is valid.

Using the assumption that the airplane has enough fuel to fly for 1 hour in clear skies, we can solve for F and T:

T > F * C + 64R

T > F * 60 + 64(0)

T > 60F

Since we assumed the airplane has enough fuel to fly for 1 hour in clear skies, T must be greater than the amount of fuel consumed during that time:

T > F * 60

Combining these two inequalities, we get:

60F < T < 60F + 3360

Now we can choose any value of F between 0 and 64 that satisfies the inequality, and choose a value of T that is greater than 3360 + 60F. For example, we can choose:

F = 30 (assuming a fuel consumption rate of 30 gallons per minute in clear skies)

T = 4000 gallons (initial amount of fuel)

Substituting these values into the inequality, we get:

56C + 64R < 9000

56(60) + 64R < 9000

3360 + 64R < 9000

64R < 5640

R < 88.125

Therefore, the airplane can fly for 88.125 minutes (or approximately 1 hour and 28 minutes) through rain clouds before consuming all of its fuel, if it is flying at a rate of 64 gallons per minute. And if the airplane consumes fuel at a rate of 30 gallons per minute while flying through clear skies, it has 4000 gallons of fuel before takeoff

No, the assertion made by your buddy is false. It is impossible to utilize the parallelogram opposite sides theorem (Thm. 7.3) to demonstrate itself. You must employ known facts and theorems rather than the theorem you are attempting to show in order to prove a theorem.

If your buddy is utilizing the SSS congruence theorem (Thm. 5.8) and the parallelogram opposite sides theorem (Thm. 7.3) to demonstrate the theorem, they are not offering a proper proof since they are employing the theorem they are attempting to demonstrate as part of the proof itself. This results in a circular argument and is invalid as evidence

The parallelogram opposing sides theorem has to be proven using other well-known facts and theorems, like the definition of a parallelogram, the definition of congruent figures, and other relevant theorems and postulates from geometry.

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Therefore, the vector form of the equation y = x² - 8x + 15 is y = (x - 4)² + 14. The vertex of the parabola is at the point (4, 14).

To convert the quadratic equation y = x² - 8x + 15 from standard form to vertex form, we need to complete the square by adding and subtracting a constant term. Here's the step-by-step explanation:

Factor the coefficient of x²: The coefficient of x² is 1, so we don't need to factor it.

Group the x terms: Rewrite the quadratic equation as y = (x² - 8x) + 15.

Complete the square: To complete the square, we need to add and subtract a constant term that will make the expression inside the parentheses a perfect square trinomial. The constant we need to add is half of the coefficient of x, squared: (8/2)² = 16.

y = (x² - 8x + 16 - 16) + 15 // add and subtract 16

y = (x - 4)² - 1 + 15 // factor and simplify

Simplify: Now we can simplify the expression by combining the constants -1 and 15 to get 14.

y = (x - 4)² + 14

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Answer:

Correlation coefficient = 0.945 ( approx) and weight of a student increases as the height of the student increases.

Step-by-step equation:

Here, value of x are   58, 59, 60, 62, 63, 64, 66, 68, 70

Value of y are,     122, 128, 126, 133, 145, 136, 144, 150, 151.

∑x = 570, ∑y= 1236, ∑ = 36234, ∑ = 170694

∑xy=78617

Thus the correlation coefficient,

Where n is the number of the term.

here n = 9

thus, correlation coefficient

r =

Thus, r= 0.94452987512

Which is closed to 0.95 and greater than 1

Therefore, weight of a student increases as the height of the student increases.

Answer:

yes

Step-by-step explanation:

2 bases 3 rectangles, folds properly.

Answer is attached

hope it helps you ⬆️

An equation for the volume of the prism as a function of the height is Volume = h³ + 2h² - 15h.

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The expansion of y = 1/(1 - x) using the binomial theorem is: y = 1 + x + x^2 + x^3 + x^4 + . (infinite series representation). The binomial theorem is a powerful mathematical tool that allows us to expand expressions of the form (a + b)^n, where n is a positive integer.

In this case, we have y = 1/(1 - x), which can be rewritten as y = (1 - x)^(-1). We can use the binomial theorem to expand this expression as follows:

(1 - x)^(-1) = 1 + (-1)x + (-1)(-2)x^2/2! + (-1)(-2)(-3)x^3/3! + .

The binomial theorem tells us that each term in the expansion can be calculated using the formula:

C(n, k) * a^(n - k) * b^k

where C(n, k) is the binomial coefficient given by n! / (k! * (n - k)!), a is the coefficient of the first term (in this case, 1), b is the coefficient of the second term (in this case, -x), and k ranges from 0 to n.

Applying this formula to our expression, we can simplify each term in the expansion:

(1 - x)^(-1) = 1 + (-1)x + (-1)(-2)x^2/2! + (-1)(-2)(-3)x^3/3! + .

= 1 - x + x^2/2 - x^3/6 + .

This expansion gives us a power series representation of y = 1/(1 - x). Each term in the series corresponds to a power of x, and the coefficients of the terms are determined by the binomial coefficients. By including more terms in the expansion, we can obtain increasingly accurate approximations of the original expression.

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