What does 2^10/4^42 equal

Answer:

244

Step-by-step explanation:

\(544 - 300 = \\ 244\)

Answer:

Step-by-step explanation:

What is the margin of error if the sample size is 100, sample mean is 68.0, and standard deviation is 4.0

The Margin of error formula =

± z score × s/√n

Where s = standard deviation= 4

n= Number for samples = 100

z = z score of confidence interval

Margin of error = ± z × 4/√100

Margin of error = ±z × 4/10

=± z × 2/5

= ± z × 0.4

= ± 0.4z

Margin of error = ± 0.4z

Answer:

Wind speed = 30 mph

Plane speed = 270 mph

Step-by-step explanation:

Given that :

Distance = 600 miles

Let speed of airplane = a ; speed of wind = b

Net speed ; with wind = a + b

Net speed against wind = a - b

Time taken with wind = 2 hours

Time taken against wind = 2.5 hours

Recall :

Speed = distance / time ; distance = speed * time

(a + b) * 2 = (a - b) * 2.5

2a + 2b = 600

a + b = 300 - - - (1)

a = 300 - b

2.5a - 2.5b = 600

a - b = 240 - - - (2)

300 - b - b = 240

300 - 2b = 240

-2b = - 60

b = 30

a = 300 - 30

a = 270

Wind speed = 30 mph

Plane speed = 270 mph

Answer:

25% of the isles are empty

Step-by-step explanation:

48/12 is 25%

Answer:

25%

Step-by-step explanation:

12 + 12 + 12 + 12= 48

if 12 isles are empty, then that is 1/4 of 48 aka 25%

Answer:

$45

Step-by-step explanation:

3x4=12

15x3=45

Answer:

\( r = 17.5 \)

Step-by-step explanation:

Given ∆TRS,

Where,

m < R = 105°

TR = s = 15

RS = t = 6

ST = r = ?

Find r using the Law of Cosines.

\( r^2 = s^2 + t^2 - 2*s*t*cos(R) \)

Plug in the values stated above into the formula

\( r^2 = 15^2 + 6^2 - 2*15*6*cos(105) \)

\( r^2 = 225 + 36 - 180*(-0.2588)\)

\( r^2 = 261 + 46.584 \)

\( r^2 = 307.584 \)

\( r = \sqrt{307.584} \)

\( r = 17.5 \) (to the nearest tenth)

Answer:

11.9 miles

Step-by-step explanation:

16 - 4.1 = 11.9

Answer:

y + 3 = 10(x + 7)

Step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

here m = 10 and (a, b ) = (- 7, - 3 ) , then

y - (- 3) = 10(x - (- 7) ) , that is

y + 3 = 10(x + 7)

Answer:

x=2. or. x=8

Step-by-step explanation:

x^2-10x+16=0. s=-10

x^2-8x-2x+16=0. p=16

x(x-8)-2(x-8)=0. [-8,-2]

(x-2)(x-8)

x=2. or. x=8

The statement means that the observed relationship between the independent variable and the dependent variable is "very unlikely to occur by chance."

In statistical analysis, the concept of statistical significance helps determine if the results obtained from a study are reliable and not due to random chance. When an effect is deemed statistically significant, it suggests that the relationship between the independent variable (the variable being manipulated or studied) and the dependent variable (the variable being measured or observed) is likely to exist in the population from which the sample was drawn.

By reaching statistical significance, the researcher can confidently conclude that the observed effect is more than just a random occurrence and has practical implications in the real world, thus lending support to the underlying hypothesis or research question.

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Therefore, it must be the case that rank (A) = cols(A) = 4.

b) Let v be an eigenvector of A corresponding to 1.

since A is a matrix, then by definition Av = 1v. Also,

we know S-AS = B,

so AS - S = -B.

Now (S - lv)B = (S - lv)(AS - S)

= S(AS-S)- lv(AS-S)

= SAS - SS - lvAS + lvs

= -lv + lvs

= l(Sv) - lv

= l(Av) - lv

= l(v) - lv

= (l-1)v.  

This means that (S-lv) is an eigenvector of B corresponding to (l-1).

Hence, s-lv is an eigenvector of B corresponding to (l-1).

c) Let {v1, v2, v3} be a linearly independent set of vectors in a vector space V.

Suppose that v3 E span {v1, v2}.

Then we can write v3 = av1 + bv2 for some scalars a and b.

Now we want to show that a = b

= 0.

Suppose not.

Then either a is not zero or b is not zero.

Without loss of generality, assume that a is not zero.

Then we can write v1 = (1/a)v3 - (b/a)v2, which shows that v1 E span {v2, v3}.

However, this contradicts the assumption that {v1, v2, v3} is linearly independent.

Hence, a = b

= 0,

which means that {v1, v2, v3} is linearly independent.

d) False, nullity(A) + rank(A) = cols(A), where cols(A) is the number of columns in A.

Since A is a 13 x 4 matrix and nullity(A) = 0, this means that rank(A)

= 4.

However, since A has only 4 columns, we know that rank(A) cannot be greater than 4.

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Answer:

Below

Step-by-step explanation:

3% = .03 in decimal      4 (yearly) periods

The effective interest and deposit amount after  3 years compounded yearly will be

3300 (1 +.03)^4   =  £ 3714.18  

Answer:

A central angle, such as angle of circle Z, is an angle whose vertex is and whose sides are radii of the circle.

Answer:

do you have a pic of the circle

Step-by-step explanation:

The  curved is surface area of the curved viewing area of the planetarium 188.4 ft²

Recall that the area of a hemisphere is of two types: The curved surface area of a hemisphere = 2r2 square units.

The total surface area of a hemisphere = 3r2 square units.

This implies that the surface area of the curved viewing area of the

planetarium is  2r²

CSA = 2*3.14 * 30 ft²

Curved surface area = 188.4 ft²

In conclusion the surface area of the curved viewing area of the

planetarium is 188.4 ft²

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The length of the walkway in feet is 15.

Any plane shape that has four equal length of sides is referred to as a square. Its area is the amount of space that it covers in a 2 dimensional plane. And the area of a square is given as;

area of a square = length x length

                           = length^2

It is measured in squared units.

Given that there are 5 square carpet tiles which covered an area of 45 square feet, then the area of one square carpet tile is;

area of one square carpet tile = total area covered/ number of tiles

                                     = 45/ 5

area of one square carpet tile = 9 square feet

But,

area of a square = length^2

9 = length^2

length = 3 feet

So that,

length of the walkway = 5 x 3

                                     = 15 feet

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The slope of the regression line is  b=61.02 and y-intercept is a=3.12

Regression analysis is a set of statistical processes used to estimate the relationships between a dependent variable and one or more independent variables. Linear regression is the most popular type of regression analysis, in which one finds the line (or a more sophisticated linear combination) that best fits the data according to a certain mathematical criterion. The ordinary least squares method, for example, finds the unique line (or hyperplane) that minimizes the sum of squared discrepancies between the genuine data and that line (or hyperplane). This enables the researcher to estimate the

Given,

The regression line is y=3.12+61.02 s

Here the slope is b=61.02

The slope indicates that the distance is increased by 61.02 yards for every one mile per hour of the speed.

And the y-intercept is a=3.12

It is the distance estimated by this model if the speed is zero miles per hour.

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I regret to inform you the answer is x = -1 :/

We can solve this three different ways.

First, because both equations are equal to variable y, we can set them equal to each other, isolate variables and constants, simplify, and then solve for x.
2x + 8 = -3x + 3
- 2x         - 2x
8 = -5x + 3
-3         - 3
5 = - 5x
Divide both sides by -5
5 / (-5) = -5x / (-5)
-1 = x or x = -1

Second, we can isolate both variables x and y on one side and constants on the other and solve for x by adding and simplifying the system of equations.
y = 2x + 8
y = -3x + 3
2x - y = -8
3x - y = -3
Pick one of equations to multiply by -1 such that we can cancel out a variable and solve for the other.
2x - y = -8
-1(3x - y = -3)
2x - y = -8
3x + y = 3
Combine like terms
2x + 3x - y + y = -8 + 3
5x + 0 = -5
5x = -5
Divide both sides by 5
5x / 5 = (-5) / 5
x = -1
In this method, you could also solve for y and then plug it into one of the equations in order to solve for x.

The third way is to place both of these equations on a graph and observe where they cross paths. This image is included below. The first equation is represented by the red line; the second equation represented by the blue. As you can see, they intersect at point (-1, 6) where the x-value is -1 and the y-value is 6.

I suggest re-reading the question once more to see if it is, indeed, asking for the x-value or if these are the equations used. If it is, try possibly placing a space between the negative and the number 1. If this also does not work, consider screenshotting and reaching out to an instructor with the mistake in the system.

Answer:

(2, 16), (3, 24), (4, 32), (5, 40)

Step-by-step explanation:

Chow,...!

Answer:

your answer would be (2, 16), (3, 24), (4, 32), (5, 40)

Step-by-step explanation:

8 * 2 = 16

8 * 3 = 24

8 * 4 = 32

8 * 5 = 40

Answer:

b i believe

Step-by-step explanation:

A 95% confidence interval for the population mean for the given survey is (24.02, 27.98).

The 95% confidence interval for the population mean can be constructed using the formula below:

x ± t∗(s/√n),

where x is the sample mean, t is the t-score with (n-1) degrees of freedom for the given confidence level, s is the standard deviation of the sample, and n is the sample size.

In this problem, we have n = 50, x = 26 weeks, and s = 6.2 weeks.

The t-score for a 95% confidence level with (n-1 = 49) degrees of freedom can be found using a t-table or a calculator. Using a t-table, we get a t-score of 2.009.

Therefore, the 95% confidence interval for the population mean is:

x ± t∗(s/√n) = 26 ± 2.009 × (6.2/√50) ≈ (24.02, 27.98)

Therefore, we can conclude that with 95% confidence, the population mean of the time it takes for executives who were laid off during a recent recession to find another position lies between approximately 24.02 weeks and 27.98 weeks.

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The time is needed between injections is 3.6 hours, i.e., the drug is to be injected again when the number of milligrams reaches 6 mg.

We have the exponential function of number of milligrams D (ht) of a certain drug that is in a patient's bloodstream h hours after the drug is injected is

\(D(h)=25 {e}^{ - 0.4 h}\)

We have to solve for h (the numbers of hours) that would have passed when the D(h) (the amount of medication in the patient's bloodstream) equals 6 mg in order to know when the patient needs to be injected again.

\(6 = 25 {e}^{ - 0.4h} \)

\( \frac{6}{25} = \frac{25}{25} {e}^{ - 0.4h} \)

\(0.24= {e}^{ - 0.4h} \)

Taking logarithm both sides of above equation , we get,

\( \ln(0.24) = \ln( {e}^{ - 0.4h)} \)

Using the properties of natural logarithm,

\( \ln(0.24) = - 0.4h\)

\( - 1.427116356 = - 0.4h\)

\(h = \frac{1.42711635}{0.4} = 3.56779089\)

=> h = 3. 6

So, after 3.6 hours, the patient needs to be injected again.

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Answer:

x=-99/56 or x=141/56

Step-by-step explanation:

We can proved that the sum of the squares of the diagonals of a parallelogram is equal to the sum of the squares of its sides.

Let's denote the vertices of the parallelogram as A, B, C, and D, with O as the midpoint of AC and BD.

First, we can see that triangles ABO and CDO are congruent by the Side-Side-Side (SSS) postulate, since they share side BD, and both have sides AB and CO of equal length due to O being the midpoint of BD. Therefore, angles AOB and COD are congruent, and we can denote their measure as θ.

Using the Law of Cosines in triangles ABO and CDO, we can express the squares of the diagonals AC and BD in terms of the sides of the parallelogram:

AC² = AB² + BC² - 2(AB)(BC)cosθ

BD² = AB² + BC² + 2(AB)(BC)cosθ

Adding these two equations together, we get:

AC² + BD² = 2(AB² + BC²)

which is the desired result. Therefore, we have shown that the sum of the squares of the diagonals of a parallelogram is equal to the sum of the squares of its sides.

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When the cosine of an angle (0) is 3/5 and the angle lies in quadrant 4, the exact value of the sine of that angle is -4/5.

To find the exact value of sin(0), we can utilize the Pythagorean identity, which states that \(sin^2(x) + cos^2(x) = 1,\) where x is an angle in a right triangle. Since the terminal side of the angle (0) is in quadrant 4, we know that the cosine value will be positive, and the sine value will be negative.

Given that cos(0) = 3/5, we can determine the value of sin(0) using the Pythagorean identity as follows:

\(sin^2(0) + cos^2(0) = 1\\sin^2(0) + (3/5)^2 = 1\\sin^2(0) + 9/25 = 1\\sin^2(0) = 1 - 9/25\\sin^2(0) = 25/25 - 9/25\\sin^2(0) = 16/25\)

Taking the square root of both sides to find sin(0), we have:

sin(0) = ±√(16/25)

Since the terminal side of (0) is in quadrant 4, the y-coordinate, which represents sin(0), will be negative. Therefore, we can conclude:

sin(0) = -√(16/25)

Simplifying further, we get:

sin(0) = -4/5

Hence, the exact value of sin(0) when cos(0) = 3/5 and the terminal side of (0) is in quadrant 4 is -4/5.

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Note the correct and the complete question is

Q- Find the exact value of sin(0) when cos(0) =3/5 and the terminal side of (0) is in quadrant 4​ ?

Answer:

x = 18.928, 5.0718

Explanation:

x = 4√3 + 12, - 4√3 +12

decimal form:

x = 18.928, 5.0718

As a result, the solid's volume in the first octant, which is restricted by the paraboloid z = 4 + 2 x + 2 y, is 9.

We must determine the limits of integration for x, y, and z in order to determine the volume of the solid in the first octant bounded by the paraboloid z = 4 + 2x + 2y + 2 and the plane z = 10.

At z = 10, where the paraboloid and plane overlap, we put the two equations equal and find z:

4 + 2x^2 + 2y^2 = 10

2x^2 + 2y^2 = 6

x^2 + y^2 = 3

This is the equation for a circle in the xy plane with a radius of 3, centred at the origin. We just need to take into account the area of the circle where x and y are both positive as we are only interested in the first octant.

Integrating over the circle in the xy-plane, we may determine the limits of integration for x and y:

∫∫[x^2 + y^2 ≤ 3] dx dy

Switching to polar coordinates, we have:

∫[0,π/2]∫[0,√3] r dr dθ

Integrating with respect to r first gives:

∫[0,π/2] [(1/2)(√3)^2] dθ

= (3/2)π

So the volume of the solid is:

V = ∫∫[4 + 2x^2 + 2y^2 ≤ 10] dV

= (3/2)π(10-4)

= 9π

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The end behavior of the polynomial y = -x³ + 2x² + x - 2 is described as follows:

The left tail points upward and the right tails points downward.

The end behavior of a polynomial function is given by the limits of the function as x approaches infinity, meaning that only the term with the highest exponent is considered.

These limits are divided into two tails, as follows:

The function in this problem is given as follows:

y = -x³ + 2x² + x - 2

At the left tail, the limit is given as follows:

lim x -> -∞ f(x) = -(-∞)³ = -(-∞) = ∞.

Hence it points upward.

At the right tail, the limit is given as follows:

lim x -> ∞ f(x) = -(∞)³ = -(∞) = -∞.

Hence it points downward.

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The expression "5 + 7 - first calculated you've at least three" is not clear and seems to contain a grammatical error. However, assuming you meant "5 + 7 - (first calculated you've at least three)," I can provide an explanation.

In the expression "5 + 7 - (first calculated you've at least three)," we need to follow the order of operations (also known as PEMDAS). PEMDAS stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

To simplify the expression, we first evaluate any operations within parentheses. However, in this case, the phrase "first calculated you've at least three" is not a valid mathematical operation or instruction.

If you provide a clear and valid expression, I would be happy to assist you in simplifying it using the order of operations.

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