what is -0.24569 rounded to the nearest hundredth?​

Answer:

A) \(f^{-1}(x)=-\frac{1}{5}x-\frac{4}{5}\)

Step-by-step explanation:

\(f(x)=-5x-4\\y=-5x-4\\x=-5y-4\\x+4=-5y\\-\frac{1}{5}x-\frac{4}{5}=y\\\\f^{-1}(x)=-\frac{1}{5}x-\frac{4}{5}\)

When finding the inverse of a function, we switch the values of x and y, and then solve for y, like in the 3rd-6th steps.

The common ratio is equal to 3.

The tenth term of this geometric sequence is -78,732.

The explicit-formula of this geometric sequence is aₙ = -4(3)ⁿ⁻¹.

The three terms in the sequence after the last one given are -324, -972, and -2916.

In Mathematics, the nth term of a geometric sequence can be calculated by using this mathematical expression:

aₙ = a₁rⁿ⁻¹

Where:

Next, we would determine the common ratio as follows;

Common ratio, r = a₂/a₁

Common ratio, r = -12/-4

Common ratio, r = 3.

For the explicit formula, we have:

aₙ = a₁rⁿ⁻¹ = -4(3)ⁿ⁻¹

Now, we can determine three terms in the sequence after the last one given;

a₅ = a₁r⁵⁻¹ = -4(3)⁴ = -324.

a₆ = a₁r⁶⁻¹ = -4(3)⁵ = -972.

a₇ = a₁r⁷⁻¹ = -4(3)⁶ = -2916.

f(10) = a₁₀ = a₁r¹⁰⁻¹ = -4(3)⁹ = -78,732.

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Answer:

b

Step-by-step explanation:

brainliest pls

Answer:

98°

Step-by-step explanation:

x = 53° + 45° { exterior angle of a triangle is equal to the sum of two opposite interior angles }

x = 98°

where

p = principal

r = rate

t = time

Principal is the amount of money invested for a period of t years with an interest rate r

Let's add the fractions to determine how many miles Rami run:

Therefore Rami run 2 11/24 miles. (In decimal approximation this is 2.4583 miles)

Answer:inconclusive

i tried to do it the long winded way but im stumped

Step-by-step explanation:

780-475 = 305

1% of 780 = 7.8

5% of 780 = 39

10% of 780 = 78

20% of 780 = 156

30% of 780 = 236

40% of 780 = 314

50% of 780 = 390

60% of 780 = 468

61% of 780 = 475.8

There are twο distinct x-intercepts and three zerοs (οr rοοts) fοr the functiοn f(x).

A functiοn is a mathematical cοncept that describes a relatiοnship between twο sets οf values, typically called the dοmain and the range. It is a set οf οrdered pairs (x, y) where each x-value is assοciated with a unique y-value.

Tο find the x-intercepts οf the graph οf f(x), we set f(x) equal tο zerο:

f(x) =\(x^{2}\)(x+2)(x-7) = 0

This equatiοn has three factοrs, sο there are three values οf x that make f(x) equal tο zerο. We can find these values by setting each factοr equal tο zerο:

x² = 0 => x = 0 (multiplicity 2)

x+2 = 0 => x = -2

x-7 = 0 => x = 7

Therefοre, the graph οf f(x) has x-intercepts at x = 0 (with multiplicity 2),

x = -2, and x = 7.

There are three x-intercepts, but οnly twο οf them are distinct (since x = 0 is a dοuble rοοt).

Therefοre, there are twο distinct x-intercepts and three zerοs (οr rοοts) fοr the functiοn f(x).

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The statement (p ∧ ~q) ∨ r means "either p and not q are true, or r is true." the truth value of the statement (p ∧ ~q) ∨ r is true under both conditions.

a) If p is true and q is true, then ~q is false. So, (p ∧ ~q) is false. Since r is also true, the entire statement becomes true: (false ∨ true) = true.

b) If p is false and q is true, then (p ∧ ~q) is false (both p and ~q need to be true for this part to be true). However, since r is true, the entire statement becomes true: (false ∨ true) = true.

So, the truth value of the statement (p ∧ ~q) ∨ r is true under both conditions.

Let's evaluate the truth value of the statement (p ∧ ~q) ∨ r under the given conditions:

a) p is true, q is true, and r is true.
(p ∧ ~q) ∨ r = (True ∧ ~True) ∨ True = (True ∧ False) ∨ True = False ∨ True = True
The statement is true under these conditions.

b) p is false, q is true, and r is true.
(p ∧ ~q) ∨ r = (False ∧ ~True) ∨ True = (False ∧ False) ∨ True = False ∨ True = True
The statement is true under these conditions as well.

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Answer:

Step-by-step explanation:

Hmmm.....rectangular pyramid.

Rectangular prism we get by slicing a rectangular cross-section to its base parallel.

The figures that will have a rectangular cross-section if sliced parallel to its base are rectangular prism

A rectangular prism has a rectangular base and all other faces are also rectangles.

Hence, if a slice is taken parallel to the rectangular base, it will result in a rectangular cross-section.

None of the other figures listed have a rectangular base, and therefore will not have a rectangular cross-section if sliced parallel to their base.

Triangular pyramid has a triangular base and will result in a triangular cross-section if sliced parallel to its base.

Rectangular pyramid has a rectangular base, but its other faces are triangles, so it will not result in a rectangular cross-section if sliced parallel to its base.

Triangular prism has a triangular base and will result in a triangular cross-section if sliced parallel to its base.

Hence, figures that will have a rectangular cross-section if sliced parallel to its base are rectangular prism

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The rate of constant for the above-given first-order reaction is b.) 8.77 × 10–3 h–1.

The half-life of a first-order reaction can be calculated using the equation t1/2 = ln(2)/k, where t1/2 is the half-life and k is the rate constant.

In this case, we know that the reaction goes to half completion in 79 hours. Therefore, the half-life is also 79 hours.

Plugging this into the equation, we get:

79 = ln(2)/k

Solving for k, we get:

k = ln(2)/79

Using a calculator, we can evaluate this expression to get:

k = 8.77 × 10–3 h–1

Therefore, the correct answer is b) 8.77 × 10–3 h–1.

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The interval of times which represents the middle 68% of Ryan's finishing times in the 400 meter race, using the empirical rule, is 74.5 seconds to 75.5 seconds.

According to the empirical rule, also known as 68-95-99.7 rule, the percentage of values that lie within an interval with 68%, 95% and 99.7% of the values lies within one, two or three standard deviations of the mean of the distribution.

\(P(\mu - \sigma < X < \mu + \sigma) = 68\%\\P(\mu - 2\sigma < X < \mu + 2\sigma) = 95\%\\P(\mu - 3\sigma < X < \mu + 3\sigma) = 99.7\%\)

Here we had  where mean of distribution of X is \(\mu\)  and standard deviation from mean of distribution of X is \(\sigma\).

When Ryan runs the 400 meter dash, his finishing times are normally distributed with a mean of 75 seconds and a standard deviation of 0.5 seconds.

The interval of times that represents the middle 68% of his finishing times in the 400 meter race is,

\(P(75 - 0.5 < X < 75 + 0.5) = 68\%\\P(74.5 < X < 75.5) = 68\%\)

Thus. the interval of times which represents the middle 68% of Ryan's finishing times in the 400 meter race, using the empirical rule, is 74.5 seconds to 75.5 seconds.

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After 37 bounces, the ball's height will be less than 1 foot.

The initial height of the ball is 50 feet.

After first bounce, the ball will reach a height of:

= 50 feet * (1 - 10%)

= 45 feet.

After second bounce, it will reach a height of:

= 45 feet * (1 - 10%)

= 40.5 feet.

Height decreases by 10% after each bounce.

We have to set up an equation:

50 feet * (0.9)^n < 1 foot

Simplifying:

0.9^n < 1/50

Taking the logarithm:

n * log(0.9) < log(1/50)

n > log(1/50) / log(0.9)

n > 37.1298771746

n > 37.13.

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Critical angle for the total internal reflection icrit, β =  78.28⁰

Critical angle for the total internal reflection crit, α = 17,22⁰

We have the refractive index of core, \(n_c_o_r_e\) = 1.46

We have the refractive index of clad , \(n_c_l_a_d\) = 1.4

Critical angle can be defined as the incidence angle which results in the refraction angle being equal to  at that angle of incidence.

For Total Internal Reflection to occur, the incidence angle must be greater than the critical angle.

We know that the critical angle, θ is given by:

sinθ = \(\frac{n_c_l_a_d}{n_c_o_r_e}\)

sinθ = \(\frac{1.4}{1.46}\)

sinθ = 0.959 = sin⁻¹(0.979) = 78.28⁰

β = θ = 78.28⁰

Now, for α:

\(\frac{sin(90-\alpha )}{sin\alpha } = \frac{1}{n_c_o_r_e}\)

sinα = sin(90⁰-78.28⁰) × 1.46

sinα = sin(11.72⁰) × 1.46

α = sin⁻¹(0.296)

α = 17,22⁰

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Critical angle for total internal reflection icrit β = 78.28⁰

Critical angle for total internal reflection crit, α = 17.22⁰

The refractive index of the core is ncore = 1.46.

The refractive index of clad is nclad = 1.4.

We know that the critical angle, θ is given by:

sinθ = nclad/ ncore

sinθ = 1.4/1.46

sinθ = 0.959

sin⁻¹(0.979) = 78.28⁰

β = θ = 78.28⁰

Now, for α:

sin(90- α) / sin α = 1 / ncore

sinα = sin(90⁰-78.28⁰) × 1.46

sinα = sin(11.72⁰) × 1.46

α = sin⁻¹(0.296)

α = 17.22⁰

Critical angle for icrit β = 78.28⁰

Critical angle for crit α = 17.22⁰

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The common difference is 0.42. The comparison of each ratio's successive values over time for a single firm.

Now, According to the question:

What is meant by ratio?

Therefore, simplifying the equation then we get,

if you take the ranges (y) and subtract one from the other you get 0.42.

(22.84 - 22.42)/(2 - 1) = 0.42/1 = 0.42

(23.26 - 22.84)/(3 - 2) = 0.42

(23.68 - 23.26)/(4 - 3) = 0.42

Hence, The common difference is 0.42

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Answer:

\((a)\ x = 3y - 2\)

\((b)\ y = -3x - 2\)

\((e)\ 3y - x = -2\)

Step-by-step explanation:

Given

\(y =3x -2\)

Required

Equations that can create consistent and independent systems

For a pair of equation to have consistent and independent systems, the equations must have different slopes.

An equation of the form \(y = mx + c\) has m has its slope.

In \(y =3x -2\)

\(m = 3\) --- slope

Considering the options

\((a)\ x = 3y - 2\)

Make y the subject

\(x = 3y - 2\)

\(3y = x+2\)

Divide by 3

\(y = \frac{1}{3}x+\frac{2}{3}\)

The slope is:

\(m_1 = \frac{1}{3}\)

Hence, (a) can make a consistent and independent system with \(y =3x -2\)

\((b)\ y = -3x - 2\)

The slope is:

\(m= -3\)

Hence, (b) can make a consistent and independent system with \(y =3x -2\)

\((c)\ y = 3x + 2\)

The slope is:

\(m=3\)

Hence, (c) cannot make a consistent and independent system with \(y =3x -2\)

\((d)\ 6x - 2y = 4\)

Make y the subject

\(2y = 6x -4\)

Divide by 2

\(y = 3x -2\)

The slope is

\(m =3\)

Hence, (d) cannot make a consistent and independent system with \(y =3x -2\)

\((e)\ 3y - x = -2\)

Make y the subject

\(3y = x -2\)

Divide by 3

\(y = \frac{1}{3}x -\frac{2}{3}\)

The slope is:

\(m = \frac{1}{3}\)

Hence, (e) can make a consistent and independent system with \(y =3x -2\)

Answer:

270

Step-by-step explanation:

90+45+45+110

so that is wat i think ooo

The probability of the low bid on the next intrastate shipping contract falling within the range of 20 to 25 thousand dollars can be determined by calculating the probability density function for a uniform distribution.

In this case, the low bids for intrastate shipping contracts are uniformly distributed between 20 and 25 thousand dollars. Since it is a uniform distribution, the probability density function (PDF) is constant within this range and zero outside of it. To find the probability that the next low bid falls within this range, we need to calculate the area under the PDF curve within the range of 20 to 25.

The PDF of a uniform distribution is given by 1 divided by the range of the distribution. In this case, the range is 25 - 20 = 5 thousand dollars. Therefore, the PDF is 1/5. To calculate the probability, we need to find the area under the PDF curve within the range. The area of a rectangle with width 5 and height 1/5 is simply 5 * (1/5) = 1. Therefore, the probability that the low bid on the next intrastate shipping contract falls within the range of 20 to 25 thousand dollars is 1, or 100%.

In conclusion, based on the information provided, the probability that the low bid on the next intrastate shipping contract falls within the range of 20 to 25 thousand dollars is 100%. This is because the low bids are uniformly distributed in this range, and the probability density function is constant within this interval.

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The tangent line is y=x-1 and differentiation of ln(x) is 1/x

What does differentiation in mathematics mean?

Differentiation is a technique for determining a function's derivative. In mathematics, the technique of differentiation is used to determine the instantaneous rate of change in a function dependent on one of its variables.

                            The most prevalent example is velocity, which is the rate at which a distance changes in relation to time.

The ratio of the vertical to the horizontal distance between any two points on it  is called slope of ray or line or line segment in analytical geometry.

y-y1 = m(x-x1)

If the function passes through (1,0)  and the slope equals to 1 is:

y-0 = 1(x-1)

y=x-1

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The complete question is -

Recall that in Problem 3 of the reading questions for Section 2.1, you found that if f(x) = ln(x), then f'(2) = 1/2. Use this to find a formula for the tangent line to f(x) = ln(x) at x = 2.

Answer:

627 miles north

747 miles east

Step-by-step explanation:

Bearing angles are measured east of north, so in (N, E) coordinates, the final position of the plane is ...

 (1.5 h)(650 mi/h)(cos(50°), sin(50°)) = (975cos(50°), 975sin(50°)) mi

 = (626.72, 746.89) mi

The plane will be 627 miles north and 747 miles east of its point of departure.

To find the y-coordinate of point P on the unit circle, given that its x-coordinate is 5/13, we can utilize the Pythagorean identity for points on the unit circle.

The Pythagorean identity states that for any point (x, y) on the unit circle, the following equation holds true:

x^2 + y^2 = 1

Since we are given the x-coordinate as 5/13, we can substitute this value into the equation and solve for y:

(5/13)^2 + y^2 = 1

25/169 + y^2 = 1

To isolate y^2, we subtract 25/169 from both sides:

y^2 = 1 - 25/169

y^2 = 169/169 - 25/169

y^2 = 144/169

Taking the square root of both sides, we find:

y = ±sqrt(144/169)

Since we are dealing with points on the unit circle, the y-coordinate represents the sine value. Therefore, the y-coordinate of point P is:

y = ±12/13

So, the y-coordinate of point P can be either 12/13 or -12/13.

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

8ºC below 0 is -8ºC (negative eight degrees celsius).

Below means subtract. 0 - 8 = -8.

Answer:

y = 10

Step-by-step explanation:

x = 7

2x + y = 24

y = -2x + 24

y = -2 * 7 + 24

y = -14 + 24

y = 10

Hope this helps!

Answer:

y = 10

Step-by-step explanation:

2(7) + y = 24

14 + y =24

y + 14 = 24

14 - 14 = y

24 - 14 = 10

y = 10

Hope this helped! :)

Answer:

Step-by-step explanation:

Given equation:

Step 1, subtract 7.5 from both sides:

Step 2, divide both sides by 8.5:

Correct answer choice is B

The statement is false. The existence of a scalar α such that αv is an eigenvector of a does not imply that v itself is an eigenvector of a.

A group of numbers built up in a rectangular array with rows and columns. The elements, or entries, of the matrix are the integers. In addition to numerous mathematical disciplines, matrices find extensive use in the fields of engineering, physics, economics, and statistics.

The statement is false. An eigenvector is a non-zero vector that, when multiplied by a matrix, produces a scalar multiple of itself. In other words, if v is an eigenvector of a matrix A, then Av = λv, where λ is the corresponding eigenvalue.

The statement suggests that if a is an nn matrix (presumably an n x n matrix), and a scalar α exists such that αv is an eigenvector of a, then v must also be an eigenvector of a. However, this is not necessarily true.

Let's consider a counterexample to demonstrate this. Suppose we have the 2x2 identity matrix I:

I = [[1, 0],

    [0, 1]]

In this case, any non-zero vector v will satisfy the condition αv = v for α = 1. However, not all non-zero vectors v are eigenvectors of I. In fact, the only eigenvectors of I are [1, 0] and [0, 1] with corresponding eigenvalues of 1.

Therefore, the statement is false. The existence of a scalar α such that αv is an eigenvector of a does not imply that v itself is an eigenvector of a.

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Answer:

5/12

Step-by-step explanation:

15 students went to hear the doctor speak and 21 students went to other sessions

How many students are there? 15 + 21 = 36 students

Therefore, the probability to randomly select a student that went to hear the doctor is \(\frac{15}{36}\), then simplifying it by 3 is \(\frac{5}{12}\).

If we want to express it in percentage it would be 41.6%

The value of the numerical expression (7 x 3481) will be 24,367.

Algebra is the study of algebraic expressions, while logic is the manipulation of those concepts.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to answer the problem correctly and precisely.

The numbers are given below.

7 and 3481

Then the product of the numbers 7 and 3481 will be given by putting a cross sign between them. Then we have

⇒ 7 x 3481

⇒ 24,367

The value of the numerical expression (7 x 3481) will be 24,367.

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Step-by-step explanation:

f(x)= x²-3x-8

f(-6)= (-6)²-3(-6)-8

=36+18-8

= 46

Answer:

okay i got you

x²-3x-8

now you replace every x with 6 and you have

(-6)²-3×(-6)-8

36+18-8

so f(-6)=46