What is the solution set of the quadratic inequality 6x^2+1≤0?

Answer:

1350 cm³

Step-by-step explanation:

Given 2 similar solids with sides in the ratio a : b , then

ratio of volumes = a³ : b³

Here the ratio of heights of A : B = 10 : 15 = 2 : 3 , thus

ratio of volumes A : B = 2³ : 3³ = 8 : 27

let x represent the volume of B then using proportion

\(\frac{8}{400}\) = \(\frac{27}{x}\) ( cross- multiply )

8x = 10800 ( divide both sides by 8 )

x = 1350

The volume of solid  B = 1350 cm³

Answer: \(\log\dfrac{x^2z^2}{y}\)

Step-by-step explanation:

Properties of logarithm:

\((i)\ \ n\log a = a^n\\\\ (ii)\ \ \log m +\log n =\log (mn)\\\\ (iii)\ \ \log m-\log n =\log\dfrac{m}{n}\)

Consider,

\(2\log x-\log y+2 \log z\\\\ =\log x^2-\log y+\log z^2\ \ \ \ \text{[By (i)]}\\\\= \log x^2+\log z^2-\log y\\\\=\log(x^2z^2)-\log y\ \ \ \ [\text{By } (ii) ]\\\\=\log(\dfrac{x^2z^2}{y}) \ \ \ \ [\text{By (iii)}]\)

Took the test, the answer is (xz)^2/y

The solution to the given system of equations is x = 2, y = -1, and z = 1.

To solve the system of equations, we can use methods such as substitution or elimination. Here, we will use the method of elimination to find the values of x, y, and z.

First, let's eliminate the variable x by multiplying equation (1) by 2 and equation (3) by -1. This gives us:

2x + 4y - 2z = -6 (4)

-x + y - z = -4 (5)

Next, we can subtract equation (5) from equation (4) to eliminate the variable x:

5y - z = 2 (6)

Now, we have a system of two equations with two variables. Let's eliminate the variable z by multiplying equation (2) by 2 and equation (6) by 1. This gives us:

4x - 2y + 2z = 10 (7)

5y - z = 2 (8)

Adding equation (7) and equation (8), we can eliminate the variable z:

4x + 5y = 12 (9)

From equation (6), we can express z in terms of y:

z = 5y - 2 (10)

Now, we have a system of two equations with two variables again. Let's substitute equation (10) into equation (1):

x + 2y - (5y - 2) = -3

x - 3y + 2 = -3

x - 3y = -5 (11)

From equations (9) and (11), we can solve for x and y:

4x + 5y = 12 (9)

x - 3y = -5 (11)

By solving this system of equations, we find x = 2 and y = -1. Substituting these values into equation (10), we can solve for z:

z = 5(-1) - 2

z = -5 - 2

z = -7

Therefore, the solution to the given system of equations is x = 2, y = -1, and z = -7.

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Answer:

19.5 kilometers

Step-by-step explanation:

to find how much he ran we can multiply the two numbers

26 * 0.75 is 19.5

he only ran 19.5 kilometers

Answer:

I can help but im going to need a question

Step-by-step explanation:

We need the question so we are able to help :P

Answer:

Step-by-step explanation:

Zero exponent numbers = 1

When you try to multiply an exponent by zero, it equals one.

Negative exponents is just a 1/x

Negative just flips over the equation.

For example, 9^-1

1/9^1

1/9

Answer:

Step-by-step explanation:

Zero Exponent Property: The zero exponent rule states that when a nonzero number is raised to the power of zero, it equals 1.

Example:  x^0 = 1

Negative Exponent Properties: the negative exponent rule tells us that a number with a negative exponent should be put to the denominator, and vice verse. It also describes how many times we have to multiply the reciprocal of the base.

An example of negative exponents is \(3^{-2}\).

Answer:

The manager predicts that 3 less hats will be sold for every $1 increase in price. For what prices can the manager predict that at least 50

Step-by-step explanation:

The manager can predict $26 that at least 80 hats will be sold.

Ratio basically compares quantities, that means it shows the value of one quantity with respect to the other quantity.

If a and b are two values, their ratio will be a:b,

Given that,

Cost of one hat = $16.

And number of hats sold by manager = 120.

Also, given that,

if $1 increases 4 fewer hats will be sold.

To find the price when 80 hats will be sold.

40 fewer hats should be sold.

4 fewer hats increases $1.

40 fewer hats will increase $1 x 10 = $10.

So the price of new price of hat = 16 + 10 = $26,

At $26 per hat the manager can sell at least 80 hats.

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Answer:

in equation form it is - 8 n ≥ 9

Step-by-step explanation:

Answer:17

Step-by-step explanation:

-8+17=9

The symmetry of the distribution depends on the probability of success and the number of trials, as it can be skewed when the probability of success is not equal to 0.5.

A binomial experiment is characterized by certain features, and among the statements provided, the two that accurately describe these features are:
1. Trials are independent: In a binomial experiment, each trial is conducted independently of one another, meaning the outcome of one trial does not affect the outcome of any other trial. This independence ensures that the probability of success remains constant across all trials.
2. The outcome of a trial can be classified as either a success or a failure: In a binomial experiment, there are only two possible outcomes for each trial - success or failure. This simplifies the experiment's setup and makes it easier to calculate probabilities, as it focuses on the number of successful outcomes out of a fixed number of trials.
The other two statements are not accurate descriptions of a binomial experiment. The trials do not represent selection without replacement, and the distribution is not always symmetrical.

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As the length of confidence interval for population mean decreases, degree of confidence in interval's actually containing population mean is option b. increases.

This is because the length of the confidence interval is determined by the level of confidence and the sample size.

With a larger sample size leading to a narrower interval.

As the interval becomes narrower, it becomes more precise and therefore more likely to contain the population mean.

So, if keep the same level of confidence and increase the sample size.

The confidence interval will become narrower, increasing our degree of confidence in its ability to contain the population mean.

Conversely, if keep the same sample size and decrease the level of confidence, the interval will also become narrower.

But will be less confident in its ability to contain the population mean.

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To find the radius of convergence, we can use the ratio test.

Let's apply the ratio test to the series:

sigma^[infinity]_n=1 4(−1)^n nx^n

The ratio test tells us that the series converges if the limit of the absolute value of the ratio of the (n+1)th term to the nth term is less than 1:

lim n -> infinity |a_n+1 / a_n| < 1

where a_n = 4*(-1)^n * n * x^n.

Let's compute the ratio of the (n+1)th term to the nth term:

|a_n+1 / a_n| = |4*(-1)^(n+1) * (n+1) * x^(n+1) / (4*(-1)^n * n * x^n)|

             = |(n+1) / n| * |x|

             = (n+1) / n * |x|

We want to find the values of x for which the above limit is less than 1. So we need to solve the inequality:

lim n -> infinity (n+1) / n * |x| < 1

Taking the limit as n approaches infinity, we get

lim n -> infinity (n+1) / n * |x| = |x|

lim n -> infinity (n+1) / n * |x| = |x|

So the inequality reduces to:

|x| < 1

Therefore, the radius of convergence R is 1.

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Answer:

Ray ZY and Ray YX are the arms

Step-by-step explanation:

A helpful analogy is that an ARM starts at the SHOULDER and ANGLES start at the VERTEX, therefore Ray ZY and Ray YX are the arms of angle ZYX.

Answer:

1 1/6 gallons will paint the whole wall

Step-by-step explanation:

7/ 10 gallon paints 3/5 of wall

x gallon will paint 1/1 of wall

7/10 * 1 = x * 3/5

7/10 = 3x/5

3x * 10 = 5 * 7

30x = 35

x = 35/30

x = 7/6 = 1 1/6 gallons

Answer:

AB = 5

Step-by-step explanation:

If the triangle is isosceles, then it has two equal sides, which must be facing the equal angles of the triangle (in our case the sides facing angles; \(\angle A\)  and  \(\angle C\)) . That means that side AB equal side BC, then you can say:

\(AB=BC\\3x-4=5x-10\\10-4=5x-3x\\6=2x\\3=x\)

Now, if x=3, then using the formula for side AB they gave you:

\(AB=3x-4=3(3)-4=9-4=5\)

Answer:

5 units.

Step-by-step explanation:

Because the triangle is isosceles the 2 sides opposite the equal angles are congruent.

AB = BC so:

3x - 4 = 5x - 10

10 - 4 = 5x - 3x

2x = 6

x = 3.

So the length of AB = 3(3) - 4 =  5 units.

Answer:

  y ≈ 60.6 units

Step-by-step explanation:

Given a triangle with angles 18° and 117°, and sides 21 opposite 18° and y opposite 117°, you want to know the value of y.

The law of sines tells you the ratios of side length to the sine of the opposite angle are the same for all side/angle pairs in the triangle.

  y/sin(117°) = 21/sin(18°)

  y = 21·sin(117°)/sin(18°) ≈ 60.55

The value of y is about 60.6 units.

Given the method given to calculate an outlier, the method does not identify 7.5 miles as an outlier.

An outlier is either very much larger or smaller than the rest of the data in the dataset.  In this dataset: 1, 2, 1000. 1000 is an outlier.

Outlier = 1.5 x interquartile range

Interquartile range = q3 - q1

1.5 x (3.8 - 2.6) = 1.8

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It take 10.374 days for the sample to be 15% of the initial amount

Radioactivity decay half life formula:

                                                    N= \(N_{0} (\frac{1}{2} )^{t/t_{1/2} }\)

                     N = Quantity remaining

                     \(t_{1/2}\) = half life

                     t = time elapsed

                    \(N_{0}\) = initial amount

given,

        Half-life of radon-222 is 3.8 days

                        \(t_{1/2}\) = 3.8 days

        Initial amount of sample = 34 gm

                      15 % of 34 gm = 15 x 34 /100

                                 =  5.1 gm

               Quantity remaining = 5.1 gm

                           = 5.1 gm

                  Using the above formula

                                                          N= \(N_{0} (\frac{1}{2} )^{t/t_{1/2} }\)

                        5.1 = 34x \(0.5^{t/3.8}\)

                       \(0.5^{t/3.8}\) = 5.1/34

                         \(0.5^{t/3.8}\) = 0.15

                     taking ln both side

                       ln( \(0.5^{t/3.8}\)  ) = ln (0.15 )

                     t/3.8  ln (0.5) = ln (0.15)

                          t/3.8  = ln (0.15) /  ln (0.5)

                                    = 2.73

                          t = 3.8 x 2.73 days

                              = 10.374 days

It take 10.374 days for the sample to be 15% of the initial amount.

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Answer:

18 days

Step-by-step explanation:

Answer: 34.5

Step-by-step explanation:

50 + 10 = 60 (birthday and dog walking)

60 - 7.50 = 53.5 (paid what she owed)

52.5 - 18 = 34.5 (bought a shirt)

Answer:

1, 2, and 4 are true statements.

Step-by-step explanation:

1. The positive symbols will become negative once you removed the parenthese. For instance, 2-(3+2)=2-3-2. It’s the same in this problem. 4-2(3+7)=4-(2•3+2•7)=4-2•3-2•7

2. Distributive property. 4-2(3+7)=4+[-2(3+7)]=4+(-2•3+-2•7)

3 is false because the positive symbol is not changed into negative symbol after the parentheses were removed.

4. 4-2(3+7)=4-[2(3+7)]=4-(2•3+2•7)

To solve the initial value problem y" + 4y = 4u_n(t), where y(0) = 0 and y'(0) = 1, we will follow these steps:

a. Find the Laplace transform of the solution y(t).

The Laplace transform of the given differential equation can be obtained using the properties of the Laplace transform. Taking the Laplace transform of both sides, we get:

s^2Y(s) - sy(0) - y'(0) + 4Y(s) = 4U_n(s),

where Y(s) represents the Laplace transform of y(t) and U_n(s) is the Laplace transform of the unit step function u_n(t).

Since y(0) = 0 and y'(0) = 1, the equation becomes:

s^2Y(s) - s(0) - 1 + 4Y(s) = 4U_n(s),

s^2Y(s) + 4Y(s) - 1 = 4U_n(s).

Taking the inverse Laplace transform of both sides, we obtain the solution in the time domain:

y''(t) + 4y(t) = 4u_n(t).

b. Find the solution y(t) by inverting the transform.

To find the solution y(t) in the time domain, we need to solve the differential equation y''(t) + 4y(t) = 4u_n(t) with the initial conditions y(0) = 0 and y'(0) = 1.

The homogeneous solution to the differential equation is obtained by setting the right-hand side to zero:

y''(t) + 4y(t) = 0.

The characteristic equation is r^2 + 4 = 0, which has complex roots: r = ±2i.

The homogeneous solution is given by:

y_h(t) = c1cos(2t) + c2sin(2t),

where c1 and c2 are constants to be determined.

Next, we find the particular solution for the given right-hand side:

For t < n, u_n(t) = 0, and for t ≥ n, u_n(t) = 1.

For t < n, the particular solution is zero: y_p(t) = 0.

For t ≥ n, we need to find the particular solution satisfying y''(t) + 4y(t) = 4.

Since the right-hand side is a constant, we assume a constant particular solution: y_p(t) = A.

Plugging this into the differential equation, we get:

0 + 4A = 4,

A = 1.

Therefore, for t ≥ n, the particular solution is: y_p(t) = 1.

The general solution for t ≥ n is given by the sum of the homogeneous and particular solutions:

y(t) = y_h(t) + y_p(t)

y(t) = c1cos(2t) + c2sin(2t) + 1.

Using the initial conditions y(0) = 0 and y'(0) = 1, we can determine the values of c1 and c2:

y(0) = c1cos(0) + c2sin(0) + 1 = c1 + 1 = 0,

c1 = -1.

y'(t) = -2c1sin(2t) + 2c2cos(2t),

y'(0) = -2c1sin(0) + 2c2cos(0) = 2c2 = 1,

c2 = 1/2.

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Answer:

  24 feet

Step-by-step explanation:

Let w represent the width of the rectangle. Then its length is 2w, and its area is ...

  A = Lw

  32 = (2w)(w) = 2w^2 . . . fill in the given values

  16 = w^2 . . . . . . . . . . . . divide by 2

  4 = w . . . . . . . . . . . . . . take the square root

  8 = 2w = L . . . . . . . . . find the length

The dimensions of the yard are 8 feet long and 4 feet wide.

__

The perimeter is ...

  P = 2(L +w) = 2(8 +4) = 2(12) = 24 . . . . feet

The perimeter of the rectangular back yard is 24 feet.

Answer: A

Step-by-step explanation:

Subtract  2  from both sides of the equation ,

Simplify , Subtract the numbers , 9x  from both sides of the equation, Combine like terms, Divide both sides of the equation by the same term, then you get your solution! I hope this helps.

Answer:

They are 5 and -4

The given equation's zeroes are 5 and -4.

In quadratic equations, it is a polynomial with a degree of 2 or the maximum power of the variable is 2. It has two options because its maximum power is two.

Given the equation y=3(x-5)(x+4). The zeroes will be calculated as:-

y = 3 (x - 5 ) ( x + 4 )

y = 0

Solve the equation for the zeroes as below,

3(x-5)(x+4) = 0

( x - 5 ) = 0

x = 5

x + 4 = 0

x = -4

Therefore, the zeroes are 5 and -4.

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Answer: Greta uses 4 ounces of pasta for every 1 cup of sauce.

The property that should be used to continue simplifying the above equation is A-^1A = 1. So, correct option is C.

We can start with the equation AB = AC and multiply both sides by A^-1 on the left:

A^-1(AB) = A^-1(AC)

Using the associative property of matrix multiplication, we can simplify the left-hand side:

(A^-1A)B = (A^-1A)C

Using the fact that A^-1A = I (the identity matrix), we get:

IB = IC

Simplifying further using the fact that I times any matrix is that matrix itself, we obtain:

B = C

Therefore, the equivalent equation to AB = AC using A^-1 that simplifies to B = C is A^-1(AB) = A^-1(AC), and the property used to continue simplifying the equation is A^-1A = I.

The correct option is (C) A^-1A = 1, which is equivalent to A^-1A = I, since the identity matrix is denoted as 1 in some contexts.

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Answer:  

11.0.0035

12.39×10^-4

13.)0.00031

14.59800

15.3.6×10^9

Step-by-step explanation:

The range of the function f(x) = log5x is (-∞, +∞).The function f(x) = log5x represents the logarithm base 5 of x. To determine the range of this function, we need to consider the possible values that the logarithm can take.

The range of the logarithm function y = log5x consists of all real numbers. The logarithm function is defined for positive real numbers, and as x approaches 0 from the positive side, the logarithm approaches negative infinity. As x increases, the logarithm function approaches positive infinity.

The range of the function is the set of all possible output values. In this case, the range consists of all real numbers that can be obtained by evaluating the logarithm

log5(�)log 5 (x) for �>0 x>0.

Since the base of the logarithm is 5, the function log5x will take on all real values from negative infinity to positive infinity. Therefore, the range of the function f(x) = log5x is (-∞, +∞).

In other words, the function can output any real number, ranging from negative infinity to positive infinity. It does not have any restrictions on the possible values of its output.

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Answer: All real numbers

Step-by-step explanation:

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