Question 19 of 45
Which of the following is the inverse of H(m) if H(m) =m/5+1

Answer:

Step-by-step explanation:

1)  Test performed is a Two sided test and this because we are trying to determine the mean difference between two groups irrespective of their direction

2) Determine the P-value ( we will use a data-data analysis approach on excel data sheet while assuming Unequal variances )

                               yes             No

Mean                   94.47059   89.76471

Variance              173.2647     95.19118

Observations            17            17

df                               30

t Stat                       1.184211  

P(T<=t) one-tail 0.122814  

t Critical one-tail 1.697261

P(T<=t) two-tail        0.245782

Hence The p-value =  0.245782

3) Since P-value is too large we cannot conclude that the students’ weight are different for these two schools.

4)   The test is inconclusive; thus we cannot claim that the average weights are different.

Answer:

39.8, $51.00

Step-by-step explanation:

Step-by-step explanation:

when pulling the square root (or any other root) of a factoral term (multiplications, divisions, exponents), you need to apply it to every part of the term.

so,

sqrt(1/9) = sqrt(1)/sqrt(9) = 1/3

The Equation of parabola with focus (3,1) and directrix y = 3 is \(10x^2 + 9y^2-60x -14y+91 =0\)

A parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped. It fits several superficially different mathematical descriptions, which can all be proved to define exactly the same curves.

Here, focus (3,1) and directrix y=3

Let the locus of parabola be (x, y)

We know that, in Parabola

Distance between locus to focus = Distance between locus to directrix line

\(\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }\) = \(\frac{Ax_{1}+By_{1}+C }{\sqrt{A^2 + B^2 + C^2} }\)

\(\sqrt{(x-3)^2+(y-1)^2} = \frac{0.x+1.y-3}{\sqrt{0^2+1^2+(-3)^2} }\)

On squaring both sides, we get

\((x-3)^2 + (y-1)^2 = (\frac{y-3}{\sqrt{10} } )^2\)

\(x^2 -6x + 9 + y^2 -2y + 1 = \frac{y^2 -6y +9}{10}\)

\(10x^2 + 9y^2-60x -14y+91 =0\)

Thus, The Equation of parabola with focus (3,1) and directrix y = 3 is \(10x^2 + 9y^2-60x -14y+91 =0\)

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Answer:

(-4,-7)

Step-by-step explanation:

Adding 1 to the x and subtracting 3 from the y we get

-5+1= -4

And

-4-3= -7

Answer:

(x+3)(2x+1)

Step-by-step explanation:

2x^2 + 7x + 3

1st step) Multiply the 2 from 2x^2 with the 3

2nd step) Then when you get x^2 + 7x + 6, find the factors of 6 that add up to the 7 from 7x.

3rd step) The factors that add up to the 7 from 7x are 6 and 1. - these factors can be represented as (x+6)(x+1).

4th step) After this, since you multiplied the 2 from 2x^2 with the 3(shown in the first step), you must divide each each factor by the 2 from 2x^2.

5th step) Finally, you should get (x+3)(2x+1). - when dividing 1 and 2, the denominator(2) should be next to/multiply with x, and when dividing the numerator(6) and the 2 from 2x^2 together, you should get x+3 since 6 divided by 2 is 3.

Answer:

Option (A)

Step-by-step explanation:

Two inequalities have been given as,

y > 3x + 6 --------(1)

y < 3x - 7 ------(2)

Inequality (1) shows the solution area shaded in blue, means all the solutions for the inequality will lie in the blue area.

Similarly, solutions of inequality (2) will lie in red area.

No common area for the inequalities.

Therefore, system of inequalities will have no solution.

Option (A) will be the answer.

Answer:

A dog needs 4/3 liters of water 2/5 of a day, Therefore

he'll need 4/3 liters for 5/2 day or

4/3 * 5/2 = 20/6 = 10/3 liters or 3 and 1/3 liters per day

Step-by-step explanation:

The slope of the line passing through the given points is -2.5.

To find the slope of a line passing through two points, we need to use the formula:

Slope = (Change in y) / (Change in x

We can choose any two points from the given table to find the slope of the line. Let's choose the points (4, 19) and (6, 14).

Change in y = 14 - 19 = -5

Change in x = 6 - 4 = 2

Slope = (-5) / 2 = -2.5

Therefore, the slope of the line passing through the given points is -2.5.

The slope of a line represents the steepness of the line. If the slope is positive, the line is increasing as we move from left to right. If the slope is negative, the line is decreasing as we move from left to right. A slope of 0 represents a horizontal line, while an undefined slope represents a vertical line.

In this case, the slope of -2.5 indicates that the line is decreasing at a moderate rate as we move from left to right. The higher the absolute value of the slope, the steeper the line.

It is important to note that the slope is constant for any two points on a straight line. Therefore, we can choose any other two points from the table to find the slope, and we will get the same result.

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Answer:

C. Never

Step-by-step explanation:

The legs of a right triangle are never longer than the hypotenuse. Otherwise, the legs would never connect to the hypotenuse.

Answer:

  (a)  twenty-eight ninths, square root of nineteen, cube root of eighty-eight

Step-by-step explanation:

When ordering a list of numbers by hand, it is convenient to convert them to the same form. Decimal equivalents are easily found using a calculator.

The attachment shows the ordering, least to greatest, to be ...

  \(\dfrac{28}{9}.\ \sqrt{19},\ \sqrt[3]{88}\)

__

Additional comment

We know that √19 > √16 = 4, and ∛88 > ∛64 = 4, so the fraction 28/9 will be the smallest. That leaves us to compare √19 and ∛88, both of which are near the same value between 4 and 5.

One way to do the comparison is to convert these to values that need to have the same root:

  √19 = 19^(1/2) = 19^(3/6) = sixthroot(19³)

  ∛88 = 88^(1/3) = 88^(2/6) = sixthroot(88²)

The roots will have the same ordering as 19³ and 88².

Of course, these values can be found easily using a calculator, as can the original roots. By hand, we might compute them as ...

  19³ = (20 -1)³ = 20³ -3(20²) +3(20) -1 = 8000 -1200 +60 -1 = 6859

  88² = (90 -2)² = 90² -2(2)(90) +2² = 8100 -360 +4 = 7744

Then the ordering is ...

  28/9 < 19³ < 88²   ⇒   28/9 < √19 < ∛88

Answer:

the ordering is

28/9 < 19³ < 88²   ⇒   28/9 < √19 < ∛88

Step-by-step explanation:

Answer:

154.2

Step-by-step explanation:

143 plus

156 plus

172 plus

133 plus

167 = 771

divide by 5 equals 154.2

The correct option regarding the continuity of f(x) at x = 2 is given by:

B. lim x -> 2 f(x) exists, but f(2) exist.

A function f(x) is continuous at x = a if it is defined at x = a, and the lateral limits are equal, that is, if these three conditions are respected:

\(\lim_{x \rightarrow a^-} f(x) = \lim_{x \rightarrow a^+} f(x) = f(a)\)

For this problem, the denominator of the function is:

8cos(0.5πx) + 2x²

At x = 2, the denominator of the function is:

8cos(0.5π(2)) + 2(2)² = 8cos(π) + 8 = -8 + 8 = 0 (as cos(π) = -1).

Then the function does not exist at x = 2, as the denominator is of 2.

From the graph of the function given at the end of the answer, we have that the lateral limits are as follows:

Since the lateral limits are equal, the limit exists, hence option B is correct.

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On solving the provided question, we got to know that  -Pythagoras' Theorem -  \(a^2 + b^2 = c^2 =\)\(5^2 + 8^2 = c^2\)

The square of the hypotenuse of a right triangle (90 degrees) is equal to the sum of the squares of the other two sides, according to the Pythagorean theorem. Keep in mind that BC2 = AB2 + AC2 in the triangle ABC below. where BC is the hypotenuse, AB is the base, and AC is the height (height). Keep in mind that the hypotenuse of a right triangle is its longest side.

Pythagoras' Theorem -

\(a^2 + b^2 = c^2\)

where the other two sides' lengths are a and b, and c is the length of the hypotenuse.

so

\(5^2 + 8^2 = c^2\\c^2 = 25 + 64\\c^2 = 89\\c = \sqrt{89}\)

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The theoretical probability of exactly 4 students from your school being selected as contestants out of 10 possible contestant spots is approximately 0.009.

Assuming that each member of the audience has an equal chance of being selected as a contestant, the total number of possible ways to select 10 contestants from the audience is:

\(150 $ choose 10 = 150! / (10! \times (150 - 10)!) = 2,535,316,699,000\)

To calculate the probability of exactly 4 students from your school being selected as contestants, we need to count the number of ways this can happen and divide it by the total number of possible outcomes.

There are 30 students from your school and 120 students from other schools in the audience.

We need to choose 4 students from your school and 6 students from other schools for the contestant spots.

The number of ways to do this is:

\(30 $ choose 4 \times 120 $ choose 6 = (30! / (4! \times 26!)) \times (120! / (6! \times 114!)) = 23,400,140,040,000\)

Therefore, the probability of exactly 4 students from your school being selected as contestants is:

P(4 students selected) = (number of ways to select 4 students from your school and 6 students from other schools) / (total number of ways to select 10 contestants from the audience)

P(4 students selected) = 23,400,140,040,000 / 2,535,316,699,000.

P(4 students selected) ≈ 0.00923 (rounded to 3 decimal places).

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The expression of logarithmic function, f(x) = ln (1/gᵏ) after all possible expansion is equals to the f(x) = - k × ln( g).

In mathematics, the logarithmic function is defined as inverse function to exponent function and defined as f(x) = logₐx where a is base of function. Properties of Logarithmic Functions :

We have, a natural logarithmic function, i.e., base = 10, f(x) = ln (1/gᵏ) and we have to expand it. To expand logarithms means write them as a sum or difference product of logarithms. The order to apply rules is quotient rule, product rule and then power rule. So, f(x) = ln (1/gᵏ)

applying quotient rule,

=> f(x) = ln(1) - ln( gᵏ)

Appling power rule,

=> f(x) = ln(1) - k ln( g)

Applying Zero Exponent Rule,

=> f(x) = 0 - k × ln( g)

Hence, the required expansion is f(x) = - k × ln( g).

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Answer:

m<v = m<w

Step-by-step explanation:

I do not know how to explain it. CD are parallel with those to lines. They ahve the same degree as the other two angles.

<y = <z are opposite angle.

<w + <x = 180 are suplementary angle which mean they add up to 180.

Answer:

$0.73 per pound

Step-by-step explanation:

2920 divided by 4000 (2 tons is 4000 pounds) equals 0.73

Answer:

805

Step-by-step explanation:

It's kinda hard to explain but first you would convert 23% to a decimal. To do that, move the decimal 2 places to the left, resulting in 0.23. Then multiply 3500 by 0.23 to get your answer.

The area of the park is 12 square units.

To find the area of the park, we can use the Shoelace Formula (also known as Gauss's area formula). This formula allows us to calculate the area of any polygon given the coordinates of its vertices.

The Shoelace Formula states that if we have the coordinates of the vertices of a polygon in counterclockwise order (x₁, y₁), (x₂, y₂), ..., (xn, yn), then the area (A) of the polygon is given by:

A = 1/2 × |(x₁y₂ + x₂y₃ + ... + xn-1yn + xny₁) - (y₁x₂ + y₂x₃ + ... + yn-1xn + ynx₁)|

In our case, the coordinates of the park's vertices are (-9, -9), (-3, -9), and (-6, -5). Let's calculate the area using the Shoelace Formula:

A = 1/2 × |(-9 × -9 + -3 × -5 + -6 * -9) - (-9 × -3 + -9 × -6 + -5 × -9)|

Simplifying further:

A = 1/2 × |(81 + 15 + 54) - (27 + 54 + 45)|

A = 1/2 × |150 - 126|

A = 1/2 × |24|

A = 12

Therefore, the area of the park is 12 square units.

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Answer:

---------------------

Plot the given vertices and connect.

See attached.

Then add the height CD.

The base is AB, with the length:

The height is CD, with length:

Find the area using equation:

Answer:

22 cents per mile

Step-by-step explanation:

to get this answer, divide 17.60 by 4 to get the unit rate, or the rate when x=1.

Answer:

5 men should be subtracted.

Step-by-step explanation:

This question is solved by proportions, using a rule of three.

As these measures(number of men needed and time) are inversely proportional, we multiply the lines instead of cross multiplication.

How many men should be working to complete the work in 32 days?

20 men - 24 days

x men - 32 days

Then

\(32x = 20*24\)

\(x = \frac{20*24}{32}\)

\(x = 15\)

How many men should be subtracted?

There are 20 to complete in 24 days.

15 are needed to complete in 32 days.

20 - 15 = 5

5 men should be subtracted.

The equation to represent this situation is given by 0.65x = 282.75 .

In the various mathematical formulas that are used, the equals sign is used to show that two expressions on either side of the equal sign are equal.  The meaning of the word equation and its cognates might vary slightly depending on the language.

Finding the exact values of the unknown variables that result in the given equality is the very first step in the solving of a variable equation. The values of the unknown variables that fulfil the equality are the equation's solutions, also known as the variables for which the equation must be solved. There are two sorts of equations.

Le t the original cost of the bike be x dollars.

After 35% reduction the new cost is x - (35% of x) = 0.65 x

Therefore 0.65 x = 282.75

or, x = 435

Therefore the cost of the bike is $435.

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Answer:

2   =  0

This equation has no solution.

Step-by-step explanation:

A a non-zero constant never equals zero

Answer: y ≤ 7

Step-by-step explanation:

brainlest  

Answer. i cant answer this without a pic of the slope

Step-by-step explanation:

Answer:

200

Step-by-step explanation:

26% = 0.26

52 divided by 0.26 = 200

200 and to get a decimal just move your decimal place back twice so 2.00 or 200

Answer:

h(-2) = -1

Step-by-step explanation:

h(x)=-2x-5

Let x= -2

h(-2)=-2*-2-5

      = 4 -5

h(-2) = -1

The second difference of the given number table is: Option A: -2

The second difference method can be used to determine a quadratic model.  In order for us to calculate the second difference, we will select 3 consecutive y-values, and then subtract the first y-value from the second and the second y-value form the third. Then we will find the difference of these two resulting values. That difference is what we refer to as the second difference.

Thus, Applying the second difference concept to our problem, we have:

First difference:

-4 - (-9) = 5

-1 - (-4) = 3

Thus, second difference is:

3 - 5 = -2

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