3. Calculating the mean when adding or subtracting a constant A professor gives a statistics exam. The exam has 50 possible points. The s 42 40 38 26 42 46 42 50 44 Calculate the sample size, n, and t

Answer:

4.5 miles

Step-by-step explanation:

0.5 of a mile per 1/9 of an hour.

rate x time=distance and you need to find distance for one hour not 1/9 so multiply it by 9 so

0.5*9=4.5, 1/9*9=1

rate   time   distance

4.5  *    1   =  d

4.5*1=d

4.5=d

so the distance traveled in one hour is 4.5 miles

Answer:

4.5 miles

Step-by-step explanation:

Given:

Let x be the distance Julia rides in one hour.

Create an equivalent ratio of miles to hours:

\(\implies \dfrac{1}{2}:\dfrac{1}{9}=x:1\)

\(\implies \dfrac{\frac{1}{2}}{\frac{1}{9}}=\dfrac{x}{1}\)

\(\implies \dfrac{1}{2}\times \dfrac{9}{1}}=x\)

\(\implies \dfrac{9}{2}=x\)

\(\implies x=4.5\)

Therefore, Julia rides 4.5 miles in one hour.

Answer:

603 cm³

Step-by-step explanation:

v = πr²h

v = π(4²)12

v = 3.14 * 16 * 12

v = 602.88

rounded

603 cm³

Answer:

x=6

Step-by-step explanation:

3x- 4=14

   +4 +4

    3x=18

      x=6

* Tantalum forms a face-centered cubic (fcc) unit cell with 4 atoms per unit cell.

* The density of vanadium is 5.97 g/cm^3.

The density of tantalum is 16.6 g/cm^3. The edge length of the unit cell is 330 pm. The molar mass of tantalum is 181 g/mol. The Avogadro constant is 6.022 * 10^23 mol^-1.

The density of a substance is defined as the mass per unit volume. So, the density of tantalum can be calculated as follows:

density = mass / volume

density = 1\(81 g / (6.022 * 10^23 mol) * (330 pm)^3 * (10^-12 cm^3 / pm^3)\)

density = 16.6 g/cm^3

The number of atoms per unit cell can be calculated as follows:

number of atoms = density * volume / molar mass * Avogadro constant

number of atoms = \(16.6 g/cm^3 * (330 pm)^3 * (10^-24 cm^3 / pm^3) / 181 g/mol * 6.022 * 10^23 mol^-1\)

number of atoms = 4

Therefore, tantalum forms a face-centered cubic (fcc) unit cell with 4 atoms per unit cell.

The density of vanadium can be calculated as follows:

density = \(51 g / (6.022 * 10^23 mol) * (305 pm)^3 * (10^-12 cm^3 / pm^3)\)

density = 5.97 g/cm^3

Therefore, the density of vanadium is 5.97 g/cm^3.

a) The null hypothesis (H0) states that the population average amount dispensed is equal to 8 ounces. The alternative hypothesis (Ha) states that the population average amount dispensed is different from 8 ounces.

b) To test the hypothesis, we can perform a one-sample t-test. The sample mean is 7.983 ounces, which is slightly below the hypothesized value of 8 ounces. We want to determine if this difference is statistically significant.

c) By conducting the one-sample t-test, we can calculate the p-value associated with the observed sample mean of 7.983 ounces. The p-value represents the probability of obtaining a sample mean as extreme as the observed value, assuming that the null hypothesis is true.

If the calculated p-value is less than the significance level (0.05 in this case), we reject the null hypothesis in favor of the alternative hypothesis, indicating evidence that the population average amount dispensed is different from 8 ounces. If the p-value is greater than the significance level, we fail to reject the null hypothesis, suggesting that there is not enough evidence to conclude that the population average is different from 8 ounces.

The interpretation of the p-value in this case is that it represents the probability of observing a sample mean of 7.983 ounces or a more extreme value, assuming that the true population mean is 8 ounces. A small p-value indicates that the observed sample mean is unlikely to have occurred by chance alone under the assumption of the null hypothesis. Therefore, a small p-value provides evidence against the null hypothesis and suggests that the population average amount dispensed is likely different from 8 ounces.

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Answer:

the answer is D.10

Step-by-step explanation:

The amount tied up in AR is $69434.12

The Gross Revenue, GR = $495,958.02

From the question:

The Annual Revenue, AR = 14% of GR

AR = (14/100) x $495,958.02

AR = 0.14 x $495,958.02

AR = $69434.12

The amount tied up in AR is $69434.12

Answer:

32+46=6x

96=6x

X=16

After solving the equation, the value obtained for x will be equal to 16°.

Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.

This relationship is illustrated by the left and right expressions being equal. The left-hand side equals the right-hand side is a basic, straightforward equation.

As per the information obtained in from the given figure,

The given angles are,

∠ m = 32°

∠ N = 64°

Then, the equation form will be,

32° + 64° = 6x

6x = 96°

x 96/6

x = 16°

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Answer: 591

Step-by-step explanation:

12 x 13= 156

12 x 5= 60 x 2= 120

12 x 5= 60/2= 30 x2= 60

5 x 12= 60

13 x 15= 195

195 + 60 + 60 + 120 + 156= 591

(a) the function\(V(x1, x2) = x1^2 + x2^2\) is positive definite.

(b) the function\(V(x1, x2) = x1^2 + x2^2 - 2x1x2\) is positive semi-definite.

(c)  cannot determine

(d) the function \(V(x1, x2) = 2x1^2 - 2x1x2 + 0.5x2^2\) is positive definite.

(e)  positive definite.

(a) To determine if the function \(V(x1, x2) = x1^2 + x2^2\) is positive definite, positive semi-definite, negative definite, negative semi-definite, or sign indefinite, we can consider the eigenvalues of the Hessian matrix.

The Hessian matrix for this function is:
H = [[2, 0], [0, 2]]

The eigenvalues of H are both positive (2 and 2). Since all eigenvalues are positive,

the function\(V(x1, x2) = x1^2 + x2^2\) is positive definite.

(b) For the function\(V(x1, x2) = x1^2 + x2^2 - 2x1x2\), the Hessian matrix is:
     H = [[2, -2], [-2, 2]]

The eigenvalues of H are both non-negative (0 and 4). Since the eigenvalues are non-negative,

the function\(V(x1, x2) = x1^2 + x2^2 - 2x1x2\) is positive semi-definite.

(c) For the function V(x1, x2) = -x1sin(x2) - \(x2^2\), we don't have a Hessian matrix since the function is not twice differentiable with respect to x1 and x2. Therefore, we cannot determine if it is positive definite, positive semi-definite, negative definite, negative semi-definite, or sign indefinite.

(d) The function \(V(x1, x2) = 2x1^2 - 2x1x2 + 0.5x2^2\) has the following Hessian matrix:
    H = [[4, -2], [-2, 1]]

The eigenvalues of H are 3 and 2. Since both eigenvalues are positive,

the function \(V(x1, x2) = 2x1^2 - 2x1x2 + 0.5x2^2\) is positive definite.

(e) The function V(x) = ∫0x h(y)dy, where h(y) is bounded and yh(y) > 0 for any y ≠ 0.

Since h(y) is bounded and yh(y) > 0 for any y ≠ 0, we can conclude that V(x) is positive definite.

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(a) The correct trigonometric ratio to use is the tangent ratio (tan).

(b) The trigonometric equation is tan(17°) = Opposite/Adjacent.

(c) tan(17°) = Opposite/Adjacent

tan(17°) = 150/Adjacent

Adjacent = 150/tan(17°)

Adjacent = 150/0.3045

Step-by-step explanation:

I have the feeling there is something missing here.

because all we see is

(x + 3) + 4y

and there is nothing to combine or multiply. all we can do is remove the brackets :

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

Answer:

9/12 = 4/x

Step-by-step explanation:

The height of the larger triangle is 9. The base of the larger triangle is 12. So let's make the ratio 9/12.

The height of the smaller triangle is 4. The base of the smaller triangle is x. So let's make the ratio 4/x.

Since both triangles are congruent, let's make these both equal each other to solve for x (if you need to).

Thus, it's 9/12 = 4/x.

The volume of a stack of 9 books is 1368.75 cubic inches.

To find the volume of a stack of 9 books, we first need to find the height of the stack. Since each book is 3/4 inch thick, the height of the stack is 9 times 3/4 inch, which is 6 3/4 inches.

Now we need to find the area of the base of the rectangular prism formed by the stack of books. Since each book has an area of 22 1/2 square inches, the total area of the base of the stack is 9 times 22 1/2 square inches, which is 202 1/2 square inches.

Therefore, the volume of the stack of 9 books is:

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Answer:

4%

Step-by-step explanation:

to find percentage do 37 divided by 925 helps it helps :)

sketch of the line 4x + 3y = 11, slope (-4/3),  y-intercept of the line y = 11/3

Step 1: Convert the equation to slope-intercept form (y = mx + b) by solving for y:

3y = -4x + 11

y = (-4/3)x + 11/3

Step 2: Identify the slope and y-intercept:

From the equation in slope-intercept form, we can see that the slope (m) is -4/3 and the y-intercept (b) is 11/3.

Step 3: Plot the y-intercept:

On the y-axis, mark a point at y = 11/3 (approximately 3.67). This is the y-intercept of the line.

Step 4: Use the slope to find additional points:

Using the slope of -4/3, we can find other points on the line. The slope represents the change in y for every 1 unit change in x. So, starting from the y-intercept, we can move down 4 units and to the right 3 units to find the next point, and continue this pattern to find more points.

Step 5: Connect the points:

Once you have a few points on the line, you can connect them with a straight line. Make sure the line extends beyond the plotted points to show that it continues indefinitely.

The resulting line should have a negative slope (-4/3) and be slanting downward from left to right.

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First step is to write the equation in slope-intercept form

\(x - 5y = 5\\-5y = -x+5\)      To make simplification easier, multiply negative to both sides

\(5y = x-5\\\)  Now, you must divide 5 to both sides to isolate the variable

\(y = \frac{x}{5} - 1\) To tell the slope more easily, turn \(\frac{x}{5}\) into \(\frac{1}{5} x\)

To rewrite the equation: \(y = \frac{1}{5} x - 1\)

Now, you are able to see the slope(m) being \(\frac{1}{5}\)

Next, you use the formula y=mx+b to solve for b (replace your newly found slope and points "x" and "y"

\(20 = (\frac{1}{5} *-15) + b\\20 = -3 + b\\b -3 = 20\\b = 23\)

Final Answer:   \(y = \frac{1}{5} + 23\)

Hope this helps :)

Answer:

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

According to the intersecting chords theorem, products of the lengths of the line segments on each chord are equal.

It translates to the given question in the form of the following equation:

Solve it for x:

Answer:

12 is the answer for this question

Answer:

Step-by-step explanation:

The simple interest formula is ...

  I = Prt . . . . . r is the interest rate, t is the number of years

Solving for P, we have ...

  P = I/(rt)

6 months is 1/2 year, so the principal is ...

  P = $4.38/(0.035×1/2) = $250.2857...

Rounded to the nearest dollar, the principal invested is $250.

__

Using the same approach, for 18 months, t = 18/12 = 3/2 = 1.5.

  P = $20.70/(0.023×1.5) = $600

The principal in Account B is $600.

__

First Month's Interest

Using the interest formula, the first month's interest in each account is ...

  A: I = 250×0.035×1/12 = $0.73

  B: I = 600×0.023×1/12 = $1.15

Account B earns more interest in the first month.

The value of the standard deviation of the variance S is equivalent to 250 and the value of the variance (S) is equivalent to 62500.

Given that:

2Ax = 0.08

Ax = 0.2

A fully discrete whole life insurance issued to (x) is 1000.

Firstly we have to find out the value of variance S.

Variance S = (insurance issued)^2 * [2Ax - Ax^2]/(1- Ax)^2

Variance S = (1000)^2 * [0.08 -  0.2^2]/(1- 0.2)^2

Variance S = (1000)^2 * [0.04]/.64

Variance S = (1000)^2 * .0625

Variance S = 62500

Standard deviation of S = (insurance issued) * [\(\sqrt{2Ax - Ax^2}\)]/(1- Ax)

Standard deviation = 1000 * [\(\sqrt{0.08 - 0.2^2}\)]/(1- 0.2)

Standard deviation = 1000 * 0.2/0.8

Standard deviation = 1000 * 1/4 = 250

The value of the standard deviation of the variance S is equivalent to 250 and the value of the variance (S) is equivalent to 62500.

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the solution to the given differential equation with the initial conditions is:

y1(t) = (1/2)e^(5t/6) + (1/2)e^(-5t/6)

y2(t) = (5/6)e^(5t/6) - (5/6)e^(-5t/6)

W(t) = 150 * sinh^2(5t/6)

Given the differential equation 36y″ - 25y = 0, we need to find the solution with the initial conditions y1(0) = 1, y1′(0) = 0 and y2(0) = 0, y2′(0) = 1.

First, we find the roots of the characteristic equation 36r² - 25 = 0 to obtain the values of m: r = ±5/6. Therefore, m1 = 5/6 and m2 = -5/6.

The general solution of the differential equation is given by y = c1e^(5t/6) + c2e^(-5t/6).

Let's find y1(t) with the initial conditions y1(0) = 1 and y1′(0) = 0:

y1(t) = c1e^(5t/6) + c2e^(-5t/6)

Differentiating y1(t), we get:

y1'(t) = (5/6)c1e^(5t/6) - (5/6)c2e^(-5t/6)

Substituting t = 0 and y1(0) = 1, we get:

1 = c1 + c2

Substituting t = 0 and y1'(0) = 0, we get:

0 = (5/6)c1 - (5/6)c2

Solving these equations, we find c1 = c2 = 1/2. Therefore, y1(t) = (1/2)e^(5t/6) + (1/2)e^(-5t/6).

Now, let's find y2(t) with the initial conditions y2(0) = 0 and y2′(0) = 1:

y2(t) = c1e^(5t/6) + c2e^(-5t/6)

Differentiating y2(t), we get:

y2'(t) = (5/6)c1e^(5t/6) - (5/6)c2e^(-5t/6)

Substituting t = 0 and y2(0) = 0, we get:

0 = c1 + c2

Substituting t = 0 and y2'(0) = 1, we get:

1 = (5/6)c1 - (5/6)c2

Solving these equations, we find c1 = 5/6 and c2 = -5/6. Therefore, y2(t) = (5/6)e^(5t/6) - (5/6)e^(-5t/6).

Now, let's find the Wronskian W(t) = W(y1, y2):

W(t) = | y1 y2 |

| y1' y2' |

Substituting the expressions for y1(t), y2(t), y1'(t), and y2'(t), we have:

W(t) = | (1/2)e^(5t/6) + (1/2)e^(-5t/6) (5/6)e^(5t/6) - (5/6)e^(-5t/6) |

| (5/6)e^(5t/6) - (5/6)e^(-5t/6) (25/12)e^(5t/6) + (25/12)e^(-5t/6) |

Simplifying, we find:

W(t) = 150 * sinh^2(5t/6)

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Answer:

I think that the answer is B

Answer:

i cant answer this because of my school computer but its simple

Step-by-step explanation:

Answer: x & y

              0 & -3

              1  & 5

slope : 8

y intercept : -3

50 degrees

Step-by-step explanation:

the x is 0 so 0 -50 is 50 so your answer is 50 degrees

Answer: this is correct

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

The transformation of the shape is most definitely correct.

The Answer is (x+9)^2

Answer:

-81/20

Step-by-step explanation:

Answer:

Jamie has 44 pairs of shoes

Step-by-step explanation:

Let

Jamie= x pairs of shoes

Suzie= 33 less than twice the amount of shoes Jamie has

2x - 33 = 55

Solve:

2x - 33 = 55

Collect like terms

2x = 55 + 33

2x = 88

Divide both sides by 2

2x / 2 = 88 / 2

x = 44

Jamie = x = 44 pairs of shoes

Therefore, Jamie has 44 pairs of shoes