During his major league career, Hank Aaron hit 248 more home runs than another famous baseball player hit during his career. Together they hit 1262 home runs. How many home runs did the other famous player hit?

a). The difference between the two population means is estimated at a location to be 2.7.

b). 49 different possible outcomes make up the t distribution. The margin of error at 95% confidence is 1.7.

c). The range of the difference between the two population means' 95% confidence interval is (0.0, 5.4).

d). The (0.0, 5.4) represents the 95% confidence interval for the difference among the two population means.

The variability or spread in a set of data is commonly measured by the standard deviation. The deviation between the values in the data set and the mean, or average, value, is measured. A low standard deviation, for instance, denotes a tendency for data values to be close to the mean, whereas a high standard deviation denotes a larger range of data values.

Using the equation \(x_1-x_2\), we can determine the point estimate of the difference between the two population means. In this instance, we calculate the point estimate as 2.7 by taking the mean of Sample

\(1(x_1=22.8)\) and deducting it from the mean of Sample \(2(x_2=20.1)\).

With the use of the equation \(df=n_1+n_2-2\), it is possible to determine the degrees of freedom for the t distribution. In this instance, the degrees of freedom are 49 because \(n_1\) = 20 and \(n_2\) = 30.

We must apply the formula to determine the margin of error at 95% confidence \(ME=t*\sqrt[s]{n}\).

The sample standard deviation (s) is equal to the average of \(s_1\) and \(s_2\) (3.4), the t value with 95% confidence is 1.67, and n is equal to the

average of \(n_1\) and \(n_2\) (25). When these values are entered into the formula, we get \(ME=1.67*\sqrt[3.4]{25}=1.7\).

Finally, we apply the procedure to determine the 95% confidence interval for the difference between the two population means \(CI=x_1-x_2+/-ME\).

The confidence interval's bottom limit in this instance is \(x_1-x_2-ME2.7-1.7=0.0\) and the upper limit is \(x_1+x_2+ME=2.7+1.7=5.4\).

As a result, the (0.0, 5.4) represents the 95% confidence interval for the difference among the two population means.

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Answer:

The wheel completed a total of 212 turns.

Step-by-step explanation:

A wheel has a circular form, therefore its length is given by the following formula:

\(length = 2*\pi*radius\)

Where radius is half the diameter. Applying the data from the problem to calculate the length of the wheel gives us:

\(length = 2*\pi*(\frac{1.5}{2})\\length = 1.5*\pi = 4.7124\)

Since the engine traveled a distance of 1000 metres and each turn of the wheel has 4.7124 metres, in order to calculate the number of turns the wheel made in that course we need to divide both numbers as shown below:

\(turns = \frac{1000}{4.7124} = 212.21\)

The wheel completed a total of 212 turns.

hope this helped buddy

Peace

The percentage of the following can be calculated as:

a. 6% of 34 is 2.04.

b. 17 is 50% of 34.

c. 18 is 30% of 60.

d. 7% of 49 is 3.43.

a. To find 6% of 34, you multiply 34 by 0.06 (which is the decimal equivalent of 6%). So, 6% of 34 is 34 * 0.06 = 2.04.

b. To find what percent 17 is of 34, you divide 17 by 34 and multiply by 100.

This is because "is" represents the percentage, and we need to find the percentage value of 17 out of 34. So, (17/34) * 100 = 50%. Therefore, 17 is 50% of 34.

c. To find the number that 18 is 30% of, you divide 18 by 0.30 (which is the decimal equivalent of 30%). So, 18 / 0.30 = 60. Therefore, 18 is 30% of 60.

d. To find 7% of 49, you multiply 49 by 0.07 (which is the decimal equivalent of 7%). So, 7% of 49 is 49 * 0.07 = 3.43.

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Answer:

\((f + g)(x) = ( \frac{x}{2} - 3) + (3 {x}^{2} + x - 6) \\ \\ = 3 {x}^{2} + (\frac{x + 2x}{2} ) - 9 \\ \\ = 3 {x }^{2} + \frac{3x}{2} - 9 \\ \\ \)

I hope I helped you^_^

Answer:70

Step-by-step explanation:

35*2=70

10*7=70

The equation of the line tangent to the curve \(\(x^2y^2 = 10\)\) at the point (3, 1) is y = 1.

To find the equation of the line tangent to the curve \(x^2y^2 = 10\) at the point (3, 1), we can use implicit differentiation.

Let's start by differentiating both sides of the equation with respect to x:

\(\[\frac{d}{dx}(x^2y^2) = \frac{d}{dx}(10)\]\)

Using the chain rule, we can differentiate the left-hand side as follows:

\(\[\frac{d}{dx}(x^2y^2) = 2x \cdot y^2 \frac{dy}{dx} + x^2 \cdot 2y \frac{dy}{dx}\]\)

Simplifying the right-hand side, we get:

\(\[2xy^2 \frac{dy}{dx} + 2x^2y \frac{dy}{dx} = 0\]\)

Now let's substitute the given point (3, 1) into the equation. We have x = 3 and y = 1:

\(\[2(3)(1)^2 \frac{dy}{dx} + 2(3)^2(1) \frac{dy}{dx} = 0\]\)

\(\[6 \frac{dy}{dx} + 18 \frac{dy}{dx} = 0\]\)

Combining the terms, we get:

\(\[24 \frac{dy}{dx} = 0\]\)

Dividing both sides by 24, we obtain:

\(\[\frac{dy}{dx} = 0\]\)

This equation tells us that the slope of the tangent line at the point (3, 1) is zero, indicating a horizontal line.

Now, we need to find the equation of this horizontal line. Since the slope is zero, the line is of the form y = c, where c is a constant. Since the line passes through the point (3, 1), we know that y = 1.

Therefore, the equation of the line tangent to the curve \(x^2y^2 = 10\) at the point (3, 1) is y = 1.

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Answer: 76

Step-by-step explanation: you add all the numbers than divide by the amount of numbers there is there

Answer:

76

Step-by-step explanation:

because the mean is also known as the average so according to my calculations the average of the ones that didn't study=76

Answer: x = 174, and x < 174.

Let the number be x.

Then 1/3 of the number = 1/3*x

1/3*x is decreased by 36 is the same as 1/3*x - 36

If 1/3*x - 36 is at most 22, we can write:

1/3*x - 36 is less than or equal to 22.

Therefore,

1/3*x - 36 <= 22

1/3*x - 36 = 22 (i), and 1/3*x - 36 < 22 (ii)

From (i):

1/3*x = 22 + 36 = 58, or x = 58 * 3 = 174.

From (ii):

1/3*x < 22 + 36 = 58, or x < 58 * 3 , or x < 174.

Therefore,

x = 174, and x < 174.

Therefore, the value of n that makes the system of equations true is n = 10.

Given:

p = 2n

p - 5 = 1.5n

Substituting the value of p from the first equation into the second equation, we have:

2n - 5 = 1.5n

Next, we can solve for n by subtracting 1.5n from both sides of the equation:

2n - 1.5n - 5 = 0.5n - 5

Simplifying further:

0.5n - 5 = 0

Adding 5 to both sides of the equation:

0.5n = 5

Dividing both sides by 0.5:

n = 10

Therefore, the value of n that makes the system of equations true is n = 10.

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Lol, channel be asking for a 100 dollars for a f-ing straw

True. An integer overflow attack occurs when an attacker manipulates a variable in a way that causes it to exceed its maximum value or minimum value, leading to unexpected and potentially harmful behavior.

This can happen if a programmer fails to properly check and validate the input values that are being used in their code, allowing an attacker to inject a value that triggers an overflow.

As a result, the variable may be assigned a value that is outside the intended range, leading to unpredictable behavior and potentially causing the program to crash or execute unintended code. It is important for programmers to take steps to prevent integer overflow attacks, such as validating input values and using data types with sufficient capacity to hold the expected range of values.

This occurs when an arithmetic operation results in a value that is too large to be stored in the allocated memory, causing the value to wrap around and become smaller, or even negative. This can lead to unintended consequences in a program's behavior, which an attacker can exploit to gain unauthorized access or cause other security issues.

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Answer: if this is khan academy the answer is 61

Step-by-step explanation:

Answer:

oooh i wonder.  -1

Step-by-step explanation:

X = -1

there

The height of water left in the can  is determined as 9.9 cm.

option B.

The height of water left in the can is calculated by the difference between the volume of a cylinder and volume of a cone.

The volume of the cylindrical can is calculated as;

V = πr²h

where;

V = π(4.6 cm)²(13.5 cm)

V = 897.43 cm³

The  volume of the cone is calculated as;

V = ¹/₃ πr²h

V = ¹/₃ π(5.1 cm)²( 8.7 cm )

V = 236.97 cm³

Difference in volume =  897.43 cm³ - 236.97 cm³

ΔV = 660.46 cm³

The height of water left in the can  is calculated as follows;

ΔV = πr²h

h = ΔV /  πr²

h = ( 660.46 ) / (π x 4.6²)

h = 9.9 cm

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Answer:

1st one is, Left

2nd one is, 3

3rd one is, Up

4th one is, 2

Step-by-step explanation:

The pre-image moved horizontally  

✔ left

.

The pre-image moved horizontally  

✔ 3

units.

The pre-image moved vertically  

✔ up

.

The pre-image moved vertically  

✔ 2

units.

Left 3,

3rd one is up.

4th one is 2.

You're Welcome!

Answer:

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Step-by-step explanation:

Answer:

10 3/25

Step-by-step explanation:

46/100x22 =46x22 divide by 100

1012/100

10 12/100 both twelve and hundred can be divided by 4 thus final answer is ten whole(10) and three over twenty five(3/25)

Answer:

The discount is $96

Step-by-step explanation:

To find the discount we

\( \frac{320}{1} \times \frac{30}{100} = \frac{32}{1} \times \frac{3}{1} \)

32 x 3 is equal to 96

Answer:

we have:

8x³ + mx² - 6x + n

= 8x³ - 8x² + (m + 8)x²- (m + 8)x + (m + 2)x - (m + 2) + m + 2+ n

= 8x²(x - 1) + (m + 8)x(x - 1) + (m + 2)(x - 1) + (m + n + 2)

= (x - 1)[8x² + (m + 8)x + m + 2] + (m + n + 2)

because the remainder if divided by (x-1) is 2

=> m + n + 2 = 2

⇔ m + n = 0 (1)

we also have:

8x³ + mx² - 6x + n

= 8x³ - 12x² + (m + 12)x² - 3/2.x.(m + 12) + ( 12 + 3/2.m)x - (9/4.m +  18) + n +9/4m + 18              

= 4x²(2x - 3) + 1/2.(m + 12)x(2x - 3) + (3/2m + 12).1/2.(2x - 3) + 9/4m + n + 18

= (2x - 3)(4x² + (m + 12)/2.x + 3/4m + 6) + 9/4m + n + 18

 because the remainder if divided by  (2x - 3) is 8

=> 9/4m + n + 18 = 8

⇔ 9/4m + n = -10 (2)

from (1) and (2), we have:

m + n = 0

9/4m + n = -10

=> m = -8

      n = 8

Step-by-step explanation:

Answer:

there are no equations below...

Step-by-step explanation:

A population standard deviation of 8.5 minutes. Then, the p-value is 0.0436.

We know the length of the show based on the assumption that shoppers spend an average of 8 minutes in line at the store checkout.

A sample of 100 buyers reported an average sample wait time of 8.5 minutes. For example, the population standard deviation is 3.2 minutes.

Null Hypothesis, H₀: μ =8 minutes    {means that the actual mean waiting time does not differs from the standard}

Alternate Hypothesis, Hₐ: μ ≠ 8 minutes    {means that the actual mean waiting time differs from the standard}

The test statistics that would be used here are One-sample z-test statistics as we know about the population standard deviation;

                      T.S. = x-μ/σ/√n   ~ N(0,1)

where, X = sample mean waiting time = 8.5 minutes

            σ  = population standard deviation = 3.2 minutes

             n = sample of shoppers = 100

So, test statistics  =  8.5 -8/3.2/√100

                             =  1.75

The value of t-test statistics is 1.75.

Now, the P-value of the test statistics is given by;

   P-value = P(Z > 1.71) = 1 - P(Z ≤ 1.75)

                 = 1 - 0.9568 = 0.0438

Complete Question:

A sample of 100 shoppers showed a sample mean waiting time of 8.5 minutes. Assume a population standard deviation of 3.2 minutes. What is the p-value?

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Point P₁(-8 + 9√2/2, 2√2, 4 - 3√2) is the required point on the ellipsoid whose tangent plane is perpendicular to the given line.

Given: The ellipsoid x² + 2y² + z² = 12.

To find: A point on the ellipsoid where the tangent plane is perpendicular to the line with parametric equations x=5-6, y = 4+4t, and z=2-2t.

Solution:

Ellipsoid x² + 2y² + z² = 12 can be written in a matrix form asXᵀAX = 1

Where A = diag(1/√12, 1/√6, 1/√12) and X = [x, y, z]ᵀ.

Substituting A and X values we get,x²/4 + y²/2 + z²/4 = 1

Differentiating above equation partially with respect to x, y, z, we get,

∂F/∂x = x/2∂F/∂y = y∂F/∂z = z/2

Let P(x₁, y₁, z₁) be the point on the ellipsoid where the tangent plane is perpendicular to the given line with parametric equations.

Let the given line be L : x = 5 - 6t, y = 4 + 4t and z = 2 - 2t.

Direction ratios of the line L are (-6, 4, -2).

Normal to the plane containing line L is (-6, 4, -2) and hence normal to the tangent plane at point P will be (-6, 4, -2).

Therefore, equation of tangent plane to the ellipsoid at point P(x₁, y₁, z₁) is given by-6(x - x₁) + 4(y - y₁) - 2(z - z₁) = 0Simplifying the above equation, we get6x₁ - 2y₁ + z₁ = 31 -----(1)

Now equation of the line L can be written as(t + 1) point form as,(x - 5)/(-6) = (y - 4)/(4) = (z - 2)/(-2)

Let's take x = 5 - 6t to find the values of y and z.

y = 4 + 4t

=> 4t = y - 4

=> t = (y - 4)/4z = 2 - 2t

=> 2t = 2 - z

=> t = 1 - z/2

=> t = (2 - z)/2

Substituting these values of t in x = 5 - 6t, we get

x = 5 - 6(2 - z)/2 => x = -4 + 3z

So the line L can be written as,

y = 4 + 4(y - 4)/4

=> y = yz = 2 - 2(2 - z)/2

=> z = -t + 3

Taking above equations (y = y, z = -t + 3) in equation of ellipsoid, we get

x² + 2y² + (3 - z)²/4 = 12Substituting x = -4 + 3z, we get3z² - 24z + 49 = 0On solving the above quadratic equation, we get z = 4 ± 3√2

Substituting these values of z in x = -4 + 3z, we get x = -8 ± 9√2/2

Taking these values of x, y and z, we get 2 points P₁(-8 + 9√2/2, 2√2, 4 - 3√2) and P₂(-8 - 9√2/2, -2√2, 4 + 3√2).

To find point P₁, we need to satisfy equation (1) i.e.,6x₁ - 2y₁ + z₁ = 31

Putting values of x₁, y₁ and z₁ in above equation, we get

LHS = 6(-8 + 9√2/2) - 2(2√2) + (4 - 3√2) = 31

RHS = 31

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Answer:

1/40 or .025

Step-by-step explanation:

Just flip the 5 then multiply instead of dividing.

\(\frac{1}{8}*\frac{1}{5}\)

You turn 5 into 1/5 by flipping it.

When you multiply them you get.

\(\frac{1}{40}\)

or

.025

Hope this helps! Have a blessed day!

The missing statement for the proof is;

Statement 3;S3 : 9x + 54 = 116

The missing reasons for the proofs are;

R1; Given

R2; Using Addition property of inequality

R3; Distributive property

R4; Using subtraction property of inequality

R5; Using Division property of inequality

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We are given the equation;

9(x + 6) − 41 = 75

Step 2;

Using addition property of equality, we add 41 to both sides;

9(x + 6) - 41 + 41 = 75 + 41

9(x + 6) = 116

Step 3;

Using distributive property to distribute 6 over the items in the bracket to get;

9x + 54 = 116

      9x + 54 - 54 = 116 - 54

       9x = 62

      9x/9 = 62/9

       x = 62/9

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Answer:

Find the inverse of g(x)=1/x-1+2 :

\(g^{-1} (x)=\frac{1}{x-1}\)

Let's take this problem step by step:

To find the ordered pair of the system:

⇒ must set both equations equal to each other

    ⇒ and solve for 'x'

Let's solve:

 \(x^2-2x+3=-2x+19\\x^2-2x+2x+3-19=0\\x^2-16=0\\(x+4)(x-4)=0\)

Let's find the x-values:

   \((x-4)=0\\x=4\\\\(x+4)=0\\x=-4\)

Let's find f(x)'s value for each 'x':

 \(x=4\\f(4)=-2(4)+19=-8+19=11\\\\x=-4\\f(-4)=-2(-4)+19=8+19=27\)

Answer: (4, 11), (-4,27)

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Note that the estimated maximum number of employees going to the gym at least twice a week is 675.

The sample size is 500 people, and 25% of them go to the gym at least twice a week, resulting in 0.25*500 = 125 employees.

Because the margin of error is 2%, the actual percentage of employees who go to the gym at least twice a week could range between 23% and 27%.

To compute the expected maximum number of workers who go to the gym at least twice a week, we may assume that all 2,500 employees have been polled and use the upper bound of the confidence interval

675 workers are equal to 0.27 x 2,500.

As a result, the maximum number of employees who go to the gym at least twice a week is 675.

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In equation (1) the value of y = 3/5 and In equation (2) the value of y = 5/4

In the given statement is

Solve 2x + 5y = -1 for y.

To find the value of y when x= -2

Now, Equation is 2x + 5y = -1 …..(1)

Put the value of x = -2 in eq. 1

2 (-2) + 5y = -1

-4 + 5y = -1

5y = -1 + 4

y = 3/5

Again,  Solve 2xy - x = 3 for y

To find the value of y when x = 2

Now, Equation is : 2xy - x = 3 ….(2)

Put the value of x = 2 in eq. (2)

2(2)y - 2 = 3

4y - 2 = 3

4y = 5

y = 5/4

Hence, In equation (1) the value of y = 3/5 and In equation (2) the value of y = 5/4

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(a) The mean of Z in case (a) is -60 and the variance is 400.

(b) The mean of Z in case (b) is 280 and the variance is 3600.

(c) The mean of Z in case (c) is 60 and the variance is 65.

(d) The mean of Z in case (d) is -20 and the variance is 65.

(e) The mean of Z in case (e) is 80 and the variance is 505.

To find the mean and variance of the random variable Z for each case, we can use the properties of means and variances.

(a) Z = 40 - 5X

Mean of Z:

E(Z) = E(40 - 5X) = 40 - 5E(X) = 40 - 5 * 20 = 40 - 100 = -60

Variance of Z:

Var(Z) = Var(40 - 5X) = Var(-5X) = (-5)² * Var(X) = 25 * Var(X) = 25 * (4)² = 25 * 16 = 400

Therefore, the mean of Z in case (a) is -60 and the variance is 400.

(b) Z = 15X - 20

Mean of Z:

E(Z) = E(15X - 20) = 15E(X) - 20 = 15 * 20 - 20 = 300 - 20 = 280

Variance of Z:

Var(Z) = Var(15X - 20) = Var(15X) = (15)² * Var(X) = 225 * Var(X) = 225 * (4)² = 225 * 16 = 3600

Therefore, the mean of Z in case (b) is 280 and the variance is 3600.

(c) Z = X + Y

Mean of Z:

E(Z) = E(X + Y) = E(X) + E(Y) = 20 + 40 = 60

Variance of Z:

Var(Z) = Var(X + Y) = Var(X) + Var(Y) = (4)² + (7)² = 16 + 49 = 65

Therefore, the mean of Z in case (c) is 60 and the variance is 65.

(d) Z = X - Y

Mean of Z:

E(Z) = E(X - Y) = E(X) - E(Y) = 20 - 40 = -20

Variance of Z:

Var(Z) = Var(X - Y) = Var(X) + Var(Y) = (4)² + (7)² = 16 + 49 = 65

Therefore, the mean of Z in case (d) is -20 and the variance is 65.

(e) Z = -2X + 3Y

Mean of Z:

E(Z) = E(-2X + 3Y) = -2E(X) + 3E(Y) = -2 * 20 + 3 * 40 = -40 + 120 = 80

Variance of Z:

Var(Z) = Var(-2X + 3Y) = (-2)² * Var(X) + (3)² * Var(Y) = 4 * 16 + 9 * 49 = 64 + 441 = 505

Therefore, the mean of Z in case (e) is 80 and the variance is 505.

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