Express the vector (-1,5,-6) in R^3 as a linear combination of (2,0,7),(2,4,5) and (2,-12,13).

3

Step-by-step explanation:

i need help to

Step-by-step explanation:

standard deviation of $3

Find a 98% confidence interval about the mean (one decimal place).

Is a value of X=48 unusually high or is it normal? Choose correct explanation

Answer:

Step-by-step explanation:

To differentiate the function y = x^4 - x, we will use the power rule of differentiation. The power rule states that if f(x) = x^n, then the derivative of f(x) is f'(x) = nx^(n-1).

So, for y = x^4 - x, we can find the derivative as follows:

y' = 4x^3 - 1

So, the derivative of the function y = x^4 - x is y' = 4x^3 - 1.

Answer:

Semicircle = 353.25 cm²

Step-by-step explanation:

Area of semicircle = πr²/2

substitute the values

semi circle = 3.14 × 15 × 15 / 2

Area of semicircle = 353.25 cm²

The math shows the world is designed, and that design is symmetry and spirals.

How is math found in nature What is the significance of mathematical patterns in nature?

Mathematics is seen in many beautiful patterns in nature, such as symmetry and spirals. Both are aesthetically appealing and proportional. Symmetry can be radial, where the lines of symmetry intersect a central point such as a daisy or a starfish.

Here,

If Hailey used math to describe the design in nature: the number of legs insects and spiders have, the number of petals on flowers, and even the patterns of spots on some animals. The math shows the world is designed, and that design is symmetry and spirals.

Hence, the math shows the world is designed, and that design is symmetry and spirals.

To learn more about the nature of maths from the given link

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Answer:

The 99% confidence interval estimate of the proportion of people who say that they voted is (0.6623, 0.7369).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \(\pi\), and a confidence level of \(1-\alpha\), we have the following confidence interval of proportions.

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which

z is the z-score that has a p-value of \(1 - \frac{\alpha}{2}\).

In a survey of 1002 people, 701 said that they voted in a recent presidential election.

This means that \(n = 1002, \pi = \frac{701}{1002} = 0.6996\)

99% confidence level

So \(\alpha = 0.01\), z is the value of Z that has a p-value of \(1 - \frac{0.01}{2} = 0.995\), so \(Z = 2.575\).

The lower limit of this interval is:

\(\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.6996 - 2.575\sqrt{\frac{0.6996*0.3004}{1002}} = 0.6623\)

The upper limit of this interval is:

\(\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.6996 + 2.575\sqrt{\frac{0.6996*0.3004}{1002}} = 0.7369\)

The 99% confidence interval estimate of the proportion of people who say that they voted is (0.6623, 0.7369).

Answer:

Since \(x\) is approaching 1 from the left/below, we take the part of \(f(x)\) that is defined over \(x<1\), for which we have

\(f(x) = \dfrac{x-1}{\sqrt{x-1}}\)

Since \(x\neq1\), we can simplify this to

\(f(x) = \dfrac{x-1}{(x-1)^{1/2}} = (x-1)^{1/2} = \sqrt{x-1}\)

and this is continuous at \(x=1\), so we can evaluate the limit by directly substituting \(x\).

To summarize:

\(\displaystyle \lim_{x\to1^-} f(x) = \lim_{x\to1} \frac{x-1}{\sqrt{x-1}} = \lim_{x\to1} \sqrt{x-1} = \sqrt{1-1} = \boxed{0}\)

Answer:

(d) -12

Step-by-step explanation:

3a = _____

a = -4

3(-4) = ___

3(-4) = -12

The answer is (d) -12

Answer:

1533g

Step-by-step explanation:

We know 2 apples weigh approximately 511g.

If we multiply this by three, we'll find the weight of 6 apples (because 2x3=6):

511x3=1533

Answer:

64 (if 4 x 4 x 4) or

12 (it could be any of them)

Step-by-step explanation:

Since "3" is related to l x w x h.

You can either do 4 x 4 x 4

or

4 x 3

It depends what formula (aka L x W x H).

Answer:

64

Step-by-step explanation:

= \(4^{3}\)

= (4) * (4) * (4)

= 64

Hope this helps :)

Answer:

27

Step-by-step explanation:

easy

Answer:

x= -1/5y+9/5

Step-by-step explanation:

5x+y=9

Step 1

First you need to add -y to both sides, basically subtracting y

5x+y-y= 9-y

Step 2

Divide both sides by 5, or multiply by 1/5. You want to do this because to cancel out 5, so you multiply the reciprocal, or divide the constant.

1/5*5x=-y+9/5

Then, you will get the answer

Hope this helps, sorry if it is wrong, I am just 4th grade :(

But I am sure this is correct :)

Answer:

slope intercept form: y= -6x+3

point slope form: y-0= -6(x -1/2)

Step-by-step explanation:

point slope form: y - y1 = m(x - x1)

substitute the values  y-0=-6(x-1/2)

slope intercept form:

find the slope using two given points

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

= (3 - 0) / (0 - 1/2)

= 3 / (-1/2)

= -6

substitute into equation

y= -6x+3

The value of the underlined digit is 800,000

Here, we want to get the value of the underlined digit.

The easiest way to get this is to write the given number in words

That would be;

five million, (eight hundred) and forty two thousand, one hundred and seventy three

From the above, we can see that the value of the underlined digit 8 is 800,000 (eight hundred thousand)

Answer:

48

Step-by-step explanation:

Given:

\(\textsf{Maximize}: \quad z=6x+12y\)

\(\begin{aligned}&\textsf{Subject to}: \quad &4x+5y & \leq 20\\&&8x+y &\leq 20\\&&x\geq 0, y&\geq 0\end{aligned}\)

Graph the lines:

\(\textsf{Draw the line } \;\;4x+5y=20 \;\;\textsf{and shade under the line}.\)

\(\textsf{Draw the line } \;\;8x+y=20 \;\;\textsf{and shade under the line}.\)

\(\textsf{Draw the line } \;\;x=0\;\;\textsf{and shade above the line}.\)

\(\textsf{Draw the line } \;\;y=0\;\;\textsf{and shade above (to the right of) the line}.\)

Therefore, the feasible region is bounded by the corner points:

Determine the value of z at the corner points by substituting the x and y values of the points into the equation for z:

\(\textsf{Value of $z$ at $A(0,0)$}: \quad 6(0)+12(0)=0\)

\(\textsf{Value of $z$ at $B(0,4)$}: \quad 6(0)+12(4)=48\)

\(\textsf{Value of $z$ at $C\left(\dfrac{5}{2},0\right)$}: \quad 6\left(\dfrac{5}{2}\right)+12(0)=15\)

\(\textsf{Value of $z$ at $D\left(\dfrac{20}{9},\dfrac{20}{9}\right)$}: \quad 6\left(\dfrac{20}{9}\right)+12\left(\dfrac{20}{9}\right)=40\)

Hence, the maximum value of z is 48 at B(0, 4).

Step-by-step explanation:

(8+(-2)-4)

=8-2-4

=2

(3-5)

=-2

Answer:

The answer would be C. 5 Hours

Step-by-step explanation:

Hopes this helps and good luck :)

The solution to the equation \(COS^ {X}\)-SINX=1/4 is: X ≈ 1.911 radians

What is Radian?

A radian is a unit of measurement for angles, used in mathematics and physics. It is defined as the angle subtended at the center of a circle by an arc that is equal in length to the radius of the circle. One radian is equivalent to approximately 57.3 degrees.

Rearrange the equation to get \(COS^ {X}\) = SINX + 1/4.

Square both sides of the equation to eliminate the square root:

\(COS^ {2X}\)= \(SIN^ {2X}\) + 1/2*SIN(X) + 1/16

Use the identity \(COS^ {2X}\)+ \(SIN^ {2X}\)= 1 to substitute for \(COS^ {2X}\)

1 - SIN^2(X) = SIN^2(X) + 1/2*SIN(X) + 1/16

Simplify the equation and rearrange terms:

SIN^2(X) + SIN(X) - 15/16 = 0

Solve for SIN(X) using the quadratic formula:

SIN(X) = (-1 ± sqrt(1 + 120/16))/4

Simplify the expression under the square root and evaluate both solutions:

SIN(X) = (-1 ± sqrt(129))/4

Since the range of SIN(X) is [-1, 1], only the positive solution is valid:

SIN(X) = (-1 + sqrt(129))/4

Use the identity\(COS^ {2X}\) + \(SIN^ {2X}\) = 1 to find the corresponding value of COS(X):

COS(X) = sqrt(1 - \(SIN^ {2X}\))

= sqrt(1 - (-1 + sqrt(129))^2/16)

Therefore, the solution to the equation C\(COS^ {X}\)-SINX=1/4 is:

X ≈ 1.911 radians (or approximately 109.49 degrees)

Learn more  about Radian

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Answer:

8(n+4)

Step-by-step explanation:

Answer:irdk im aorry i wish i could help because im in the same boat.

Step-by-step explanation:

Answer:

The very last one is the correct answer.

Step-by-step explanation:

1 * 3 = 3

6 * 3 = 18

Do this for the other ones and you will get it right.

Answer:

x=8 an they are at the exact opposite side

Step-by-step explanation:

Answer:

x = 4\(\sqrt{3}\) in

Step-by-step explanation:

Given a tangent and a secant to the circle from an external point, then

The square of the tangent is equal to the product of the secant's external part and the entire secant, that is

x² = 4(4 + 8) = 4 × 12 = 48 ( take the square root of both sides )

x = \(\sqrt{48}\) = \(\sqrt{16(3)}\) = \(\sqrt{16}\) × \(\sqrt{3}\) = 4\(\sqrt{3}\) ← exact value

Answer:

have a great day

god is great

The general equation of the line is,

Given:

Substitute the values of m and b into the equation, in order to obtain the equation.

Let us solve for the x-intercept and y-intercept in order to plot the graph of the line.

X-intercept

The x-intercept is the value of the x coordinate of a point where the value of y-coordinate is equal to zero.

Y-intercept

The point where a line or curve crosses the y-axis of a graph. In other words: find the y-value when x equals 0.

Hence, the points to plot the graph are (40 , 0) and (0 , 8).

Let us now plot the graph

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

Explanation:

We're told that "given that it is less than 8", so we only focus on these values {1,2,3,4,5,6,7}. There are B = 7 items in this set.

Of those, the set {1,2,3,4,5,6} are less than 7. There are A = 6 items in this set.

The probability we're after is A/B = 6/7 = 0.8571

Answer:

I just got this question in my book, and i already solved it. so just saying that i now the answer, it is 0.8571

Answer:

Step-by-step explanation:

First, simplify the question.

8 1/2 - [ 3 1/6 ÷ 5 1/3 + 11-(3 - 5/4 - 5/8 }]

then solve

Answer:

r = 3.02 cm

Step-by-step explanation:

V cone = πr²h/3

r = √(3V/πh)

r = √(3(143.56)/π(15))

r = 3.0231297

Answer:

0.8665 = 86.65% probability that the sample proportion of Democrats will be greater than 52%.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \(\mu = p\) and standard deviation \(s = \sqrt{\frac{p(1-p)}{n}}\)

Suppose 54% of the registered voters in a country are Democrats. Sample of 770.

This means that:

\(p = 0.54, s = \sqrt{\frac{0.54*0.46}{770}} = 0.01796\)

What is the probability that the sample proportion of Democrats will be greater than 52%?

This is 1 subtracted by the p-value of Z when X = 0.52. So

\(Z = \frac{X - \mu}{\sigma}\)

By the Central Limit Theorem

\(Z = \frac{X - \mu}{s}\)

\(Z = \frac{0.52 - 0.54}{0.01796}\)

\(Z = -1.11\)

\(Z = -1.11\) has a p-value of 0.1335

1 - 0.1335 = 0.8665

0.8665 = 86.65% probability that the sample proportion of Democrats will be greater than 52%.

Answer:

Elon Musk 269.7 B
Jeff Bezos: 170.15 B
Bill Gates: 130.23 B

Step-by-step explanation:

If you had a trail of 1 billion 1 dollar bills, it would stretch out to 96,900 miles.

If you did that with 100 billion 1 dollar bills, that would be 9,690,000 miles.

That is more than 300 times the circumference of the Earth.