You weigh a random sample of adult golden retrievers and get the following results: 55, 64, 58, 61, 69, 64, 59, 69, 72, and 65. Which answer gives a 98% confidence interval for the mean of the population

The amount of dry ingredients used in the cake recipe is approximately 7 cups.

We have,

3 ½ cups of flour, 2 ⅔ cups of sugar, and 1 ¾ cups of cocoa.

Now, first convert all quantity in same unit.

3 ½ cups of flour

= 3 cups + 0.5 cups

= 3 cups and 8 ounces.

and, 2 ⅔ cups of sugar

= 2 cups + 0.67 cups,

= 2 cups and 10.72 ounces.

and, 1 ¾ cups of cocoa

=1 cup + 0.75 cups

= 1 cup and 12 ounces.

So, the total amount

= 3 cups and 8 ounces + 2 cups and 10.72 ounces + 1 cup and 12 ounces = 6 cups and 14.72 ounces

= 7 cups

Therefore, the amount of dry ingredients used in the cake recipe is approximately 7 cups.

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Answer:

simple.

Step-by-step explanation:

If you know the angle of a straight line, its 180. first, subtract 180-135. this wqould be 45. therefore, the interior angle is 45. We know that a triangles area always adds to 180, so it would be 45+x+74=180. this would be x=61. to check, add the same thing, 45+74, but instead of x add 61.

The number of Kid's Launches that are possible is 128. This is solved using Combination Principle.

A combination in mathematics is a selection of elements from a set with distinct members, where the order of selection is irrelevant.

Hence,

The number of possible "Sizes" from the specified 4 sizes are ⁴C₁

The number of sorts of bun that is possible from the specified two bun types is:  ²C₁

From the four sides, the number of possible side purchases is:  ⁴C₁

Of the available four drinks, the number of the possible drinks is: ⁴C₁

Now the possible number of all lunches are:

⁴C₁ x  ²C₁ x  ⁴C₁ x  ⁴C₁

= 4 x 2 x 4 x 4

= 128

Hence the number of Kid's Lunches that are possible are 128.

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Step-by-step explanation:

1/2×13×12= 78

12×14= 132

13×14= 182

total surface area

= (78×2)+(132×2)+182

= 602 ft^2

Answer:

10.26

Step-by-step explanation:

This is the answer because:

1) 8 + 2 = 10

2) Now, just add .26 to 10 which is 10.26

Hope this helps! :D

Answer:

move over 5 to the right and 6 up

move 1 to the right and 4 down to get your answer

Amplitude is the maximum displacement of a function on a graph.

Amplitude is the maximum displacement of a function on a graph. It refers to the maximum height or distance from the baseline of a wave or oscillation.

It is often used in physics and engineering to describe the strength or size of a signal, vibration, or wave. In simple terms, it can be thought of as the "peak-to-peak" distance of a waveform, or the height of the waveform above and below the baseline.

But the minimum displacement of a function on a graph would typically be referred to as the minimum value or the "valley" of the function.

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Answer:

4.25x + 6.5y ≤ 60

y ≥ 0

x + y > 10

x ≥ 0

Step-by-step explanation:

    We will write mathematical inequalities for all the details given.

Let x represent the number of domestic packages.

    We cannot have negative packages, so x ≥ 0.

Let y represent the number of international packages.

    We cannot have negative packages, so y ≥ 0.

The employee has no more than 1 h to ship packages.

    If it takes 4.25 minutes to prepare an x package and 6.5 minutes to prepare a y package, and 1 hour is equal to 60 minutes, we can write this as 4.25x + 6.5y ≤ 60.

The employee must ship more than 10 packages.

    This means the total number of packages must be greater than 10, so x + y > 10.

The probability that the hacker guesses the password on their first try is extremely low.

What is the probability that the hacker guesses the password on his first try?

There are 26 lowercase letters, 26 uppercase letters, and 10 numerical digits, for a total of 62 possible characters for each position in the password. Since the password is 9 characters long, there are \(62^{9}\) possible passwords.

The probability that the hacker guesses the password on their first try is 1 out of the total number of possible passwords:

Probability = 1 / (\(62^{9}\))

Using a calculator, this can be simplified to approximately 1.2 x \(10^{-16}\)

Therefore, the probability that the hacker guesses the password on their first try is extremely low.

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Answer:

X is 9

Step-by-step explanation:

Answer:

the answer would be:

\(2n^3\)

Hope that helps! :)

Step-by-step explanation:

We have proved that the Newton-Raphson iteration formula for solving the equation\(x^k e^x = 0\) is given by \(x_{n+1} = (k - 1) x_n + x_n^2 / k + x_n.\)

To prove that the Newton-Raphson method for solving the equation \(x^k e^x = 0\), where k is a constant, is given by the formula

\(x_{n+1} = (k - 1) x_n + x_n^2 / k + x_n,\)

we can start by considering the iterative process of the Newton-Raphson method.

Given an initial guess \(x_n\), we want to find a better approximation \(x_{n+1}\)that is closer to the root of the equation \(x^k e^x = 0.\)

The Newton-Raphson method involves the following steps:

Calculate the function value \(f(x_n) = x_n^k e^x_n\) and its derivative \(f'(x_n) = k x_n^(k-1) e^x_n.\)

Find the next approximation x_{n+1} by using the formula:

\(x_{n+1} = x_n - f(x_n) / f'(x_n)\)

Let's apply these steps to our equation \(x^k e^x = 0\):

Calculate the function value and its derivative:

\(f(x_n) = x_n^k e^x_n\\f'(x_n) = k x_n^(k-1) e^x_n\)

Find the next approximation x_{n+1} using the formula:

\(x_{n+1} = x_n - f(x_n) / f'(x_n)\)

Substituting the function value and its derivative:

\(x_{n+1} = x_n - (x_n^k e^x_n) / (k x_n^(k-1) e^x_n)\\= x_n - (x_n^k / k)\)

Simplifying the expression by combining like terms:

\(x_{n+1} = x_n - (x_n^k / k)\\= x_n - x_n^k / k\\= (k - 1) x_n + x_n^2 / k + x_n\)

Therefore, we have proved that the Newton-Raphson iteration formula for solving the equation\(x^k e^x = 0\) is given by \(x_{n+1} = (k - 1) x_n + x_n^2 / k + x_n.\)

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Answer:

D.134

Step-by-step explanation:

Answer:

7<x<31

Step-by-step explanation:

The third side of any triangle must be more than the difference between the other two sides.

x>19-12

x>7 (or) 7<x

The third side of any triangle must be less than the sum of the other two sides.

x<19+12

x<31 (or) 31>x

Put them together.

7<x<31 (or) 31>x>7

7<x<31 are the possible values of x.

A triangle is a three-sided polygon that consists of three edges and three vertices.

Given that  side lengths of a triangle are 12, 19, and x units.

We need to find the value of x.

We know that the third side of any triangle must be more than the difference between the other two sides.

x is greater than difference of nineteen and twelve

x>19-12

x>7 (or) 7<x

The third side of any triangle must be less than the sum of the other two sides.

x<19+12

x<31 (or) 31>x

From this we get the interval as

7<x<31 (or) 31>x>7

Hence, 7<x<31 are the possible values of x.

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Answer:

36 is the final value for the equation you posted

Step-by-step explanation:

We are told that = 3 and = −2.

Let's plug these values into the equation.

= (5 ( − 2) + (2 − )^2)

= (5 (3 − 2(−2)) + (2 − 3)^2)

= (5 (3 + 4) + (−1)^2)

= (5 (7) + 1)

= 35 + 1

= 36

Answer:

\(h = 3.5\)

\(w = 7\)

\(l = 7\)

Step-by-step explanation:

Given

\(Volume = 171.5ft^3\)

Required

The dimension that requires least material

The volume is:

\(Volume = lwh\)

Where:

\(l \to length\)

\(w \to width\)

\(h \to height\)

So, we have:

\(171.5 = lwh\)

Make l the subject

\(l = \frac{171.5}{wh}\)

The surface area (A) of an open-top rectangular tank is:

\(A = lw + 2lh + 2wh\)

Substitute: \(l = \frac{171.5}{wh}\)

\(A = \frac{171.5}{wh} * w + 2*\frac{171.5}{wh}*h + 2wh\)

\(A = \frac{171.5}{h} + 2*\frac{171.5}{w} + 2wh\)

\(A = \frac{171.5}{h} + \frac{343}{w} + 2wh\)

Rewrite as:

\(A = 171.5h^{-1} + 343w^{-1} + 2wh\)

Differentiate with respect to h and w

\(A_h = -171.5h^{-2} +2w\)

\(A_w = -343w^{-2} +2h\)

Equate both to 0

\(-171.5h^{-2} +2w=0\)

Make w the subject

\(2w = 171.5h^{-2}\)

Divide by 2

\(w = 85.75h^{-2}\)

\(-343w^{-2} +2h = 0\)

Make h the subject

\(2h = 343w^{-2}\)

Divide by 2

\(h = 171.5w^{-2}\)

\(h = \frac{171.5}{w^2}\)

Substitute \(w = 85.75h^{-2}\) in \(h = \frac{171.5}{w^2}\)

\(h = \frac{171.5}{(85.75h^{-2})^2}\)

\(h = \frac{171.5}{85.75^2*h^{-4}}\)

\(h = \frac{2}{85.75*h^{-4}}\)

Multiply both sides by \(h^{-4}\)

\(h^{-4} * h = \frac{1}{85.75*h^{-4}} * h^{-4}\)

\(h^{-3} = \frac{2}{85.75}\)

Rewrite as:

\(\frac{1}{h^3} = \frac{2}{85.75}\)

Inverse both sides

\(h^3 = 85.75/2\)

\(h^3 = 42.875\)

Take cube roots

\(h = 3.5\) ---- height

Recall that: \(w = 85.75h^{-2}\)

\(w = 85.75 * 3.5^{-2}\)

\(w = 7\) --- width

Recall that: \(l = \frac{171.5}{wh}\)

\(l = \frac{171.5}{3.5 * 7}\)

\(l = 7\) --- length

Deepa makes use of the geometric property of similar triangles formed by

incident and reflected rays to determine the height of the goalpost.

Reasons:

When an object is reflected on a mirror, the angle of incidence, θ₁ is equal

to the angle of reflection, θ₂.

θ₁ = θ₂

Given that the angle, ∅₁, the incident ray of light and the angle, ∅₂, the

reflected light make with horizontal are both complementary angles, to the

angle of incident and reflection, respectively, we have;

θ₁ + ∅₁ = θ₂ + ∅₂

θ₁ = θ₂

Therefore, by subtraction property of equality, we have;

∅₁ = ∅₂

The vertical line from the top of the goalpost to the base of the goalpost

and the the vertical line from Deepa's eyes to the ground on which her feet

is standing are both perpendicular to the ground, therefore, the light from

the top of the goalpost to the mirror and to her eyes form similar triangles

by Angle Angle similarity postulate, which gives;

\(\displaystyle \frac{6.95}{9.35} = \frac{1.35}{The \ height \ of \ the \ goalpost}\)

6.95 × Height of the goalpost = 1.35 × 9.35

\(\displaystyle Height \ of \ the \ goalpost = \frac{1.35 \ m \times 9.35 \ m}{6.95 \ m} \approx 1.82 \ m\)

The height of the goalpost is approximately 1.82 meters.

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The inverse of the equation is determined as \(y = \log_{6}(-3x)\).

option D is the correct answer.

The inverse of the equation is calculated by applying the following method;

The given equation;

y = - 6ˣ/3

The inverse of the equation is calculated as;

multiply through by 3

\(-3x = 6^y\)

Take the logarithm of both sides of the equation with base -6:

\(\log_{6}(-3x) = y\)

Finally, replace y with x to obtain the inverse equation as follows;

\(y = \log_{6}(-3x)\)

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Answer:

x = -4 and y = -15

Hope This Helps!!!

Answer:

the correct answer is option C

Answer:

Hello There!!

Step-by-step explanation:

The answer is c. 12+h as sum means adding 12 and then with h.

hope this helps,have a great day!!

~Pinky~

Answer:

Approximate value of P(|X| > a)  is attached below

Ф ( 0 ) is the CDF of standard Normal variate

Step-by-step explanation:

x ~ Bin ( n, p )

E ( x ) = np ,  Var ( x ) = np ( 1 - p )

∴ Z = Iin    ( x - E(x) ) / √Var x )   ~ N ( 0, 1 )  ( this is the standard normal Variate)

        n-1∞

Find the approximate value of P(|X| > a)

Ф ( 0 ) is the  CDF of standard Normal variate

attached below is the remaining part of the solution

Answer:

- 23

Step-by-step explanation:

When you see a negative number behind a minus sign, turn the minus sign into a plus sign. It's the easiest way to figure out how to solve those types of problems.

Answer:

-23

Step-by-step explanation:

-35-(-12) = -35+12 = -23

The correct answers are:

Functions are expressions separated by an equal sign. They have both dependent and independent variables.

* Lets explain how to solve the problem

- The table of the function has two column

# First column labeled x with entries:

 -6 , 7 , 4 , 3 , -5

# Second column labeled f(x) with entries:

  8 , 3 , -5 , -2 , 12

∴ The ordered pairs of the function f(x) are:

 (-6 , 8) , (7 , 3) , (4 , -5) , (3 , -2) , (-5 , 12)

* Lets complete the missing

∵ The value of x in the first row is -6

∵ The value of f(x) in the first row is 8

∴ The function notation in the 1st row is f(-6) = 8

- The ordered pair given in the first row of the table can be

 written using function notation as f(-6) = 8

∵ The ordered pair whose x = 3 is (3 , -2)

∴ The value of f(x) when x = 3 is -2

∴ f(3) = -2

∵ The ordered pair whose f(x) = -5 is (4 , -5)

∴ The value of x when f(x) = -5 is 4

∴ f(x) = -5 when x is 4

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The line that goes between the coordinates (-6, 5) & (-3, -3) has the equation y = -8/3 x + 13, as stated in the question.

A line is an infinitely long, completely straight, one-dimensional form that has no thickness and may be drawn in both directions. In order to stress that a line has no "flutters" anywhere along its length, it is occasionally referred to as a straight line or, more formally, a straight line (Casey 1893).

y - y1 = m (x - x1)

By using formula :

m = (y2 – y1) / (x2 - x1)

In other (x1, Y1)& are the two pairs on the line (x2, y2).

m = ( -3 - 5) / (-3 - (-6)) = (-8) / (-3 + 6) = -8 / 3

Due to this reason, the line has a slope of -8/3.

Afterwards when, we may input either points (-6, 5) and slope (8/3), respectively, into the generate the result of both the line to obtain:

y - 5 = -8/3 (x - (-6))

Expanding the right-hand side, we get:

y - 5 = -8/3 x + 8

Finally, rearranging the terms, we get:

y = -8/3 x + 8 + 5

y = -8/3 x + 13

Consequently, the line's equation becomes y = -8/3 x + 13 and it passes through to the coordinates (-6, 5) & (-3, -3).

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The complete question is: Complete the equation of the line through (-6,5)(−6,5)left parenthesis, minus, 6, comma, 5, right parenthesis and (-3,-3)(−3,−3)left parenthesis, minus, 3, comma, minus, 3, right parenthesis.

The solution to the equation 125x³ - 27 = 0 is (5x−3)(25x ^2 +15x+9)

An equation is a mathematical expression that contains an equals symbol. Equations often contain algebra. Algebra is used in mathematics when you do not know the exact number in a calculationsolving the equation 125x³ - 27 = 0 by grouping

Rewriting 125x^ 3 −27 as (5x) ^3 −3³

The difference of cubes can be factored using the rule:: a ^3 −b^ 3 =(a−b)(a^ 2 +ab+b^ 2 )

Polynomial 25x^ 2 +15x+9 is not factored since it does not have any rational roots.

Hence, (5x−3)(25x ^2 +15x+9)

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Gauss's approach consists in group highest terms with lowest terms

a. 1+ 2+ 3+ 4 + ... +39

(1 + 39) + (2+38) + (3+37) + ... + (19+21) + 20

There are 19 terms in parentheses, all equal to 40. Then, the sum is equal to:

19*40 + 20 = 780

b. 1+3+5 + 7 + ... + 2409

(1+2409) + (3+2407) + (5+2405) + ... + (1203+1207) + 1205

there are (1203+1)/2 = 602 terms equal to 2410. Then, the sum is equal to:

602*2410 + 1205 = 1452025

c. 3+ 6 + 9 + ... + 300

(3+297) + (6+294) + (9+291) + ... + (147+153) + 150 + 300

there are 147/3 = 49 terms equal to 300. Then, the sum is equal to:

49*300 + 150 + 300 = 15150

d. 1000 +995 +990 + ... + 5

1000 + (995+5) + (990+10) + ... + (505+495) + 500

the sum has 1000/5 = 200 terms, then there are 99 terms in parentheses, all of them equal to 1000. Then, the sum is equal to:

1000 + 99*1000 + 500 = 100500

Answer:

5x - 63 = 6

Step-by-step explanation:

Okay, first step, let's get all fractions having a common denominator, to do this, multiply 2/3 by 3 to get 6/9. Now, we have 5/9x-7=6/9. To make these into whole numbers, we can multiply the whole equation by the denominator (9). 5/9x multiplied by 9 is 5. 7 multiplied by 9 is 63. 6/9 multiplied by 9 is 6. Now we have 5x-63=6. If I were to simplify the equation, it would require decimals, so I'll leave it at this, but the equation simplified is x=13.8.

Answer:

-8

Step-by-step explanation:

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

            = ( f-4) / (-8 - -6)      =  6

                  (f-4) / -2    = 6

                    f-4 = -12

                     f = - 8

Answer:

f = -8

Explanation:

Find slope:

\(\sf slope: \dfrac{y_2 - y_1}{x_2- x_1} = \dfrac{\triangle y}{\triangle x} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points\)

Here given:

Inserting into slope formula:

\(\sf \rightarrow \dfrac{4-f}{-6-(-8) } = 6\)

\(\sf \rightarrow \dfrac{4-f}{2 } = 6\)

\(\sf \rightarrow 4-f = 12\)

\(\sf \rightarrow -f = 12-4\)

\(\sf \rightarrow -f =8\)

\(\sf \rightarrow f =-8\)