Salazar made an investment in 140 shares of stock in a no-load fund for $2,993.20. after one year the stock had a net asset value of $24.53 per share. if salazar redeems all 140 shares, which of the following is a correct statement? a. salazar will have a loss of $441. b. salazar will have a profit of $441. c. salazar will have a profit of $3,434.20. d. there is not enough information to calculate profit or loss.

Answer:

Electric force = 8.20x10⁻⁸ N

Gravitational force = 3.61x10⁻⁴⁷ N

Step-by-step explanation:

1. The electric force can be found using the following equation:

\( F_{e} = \frac{Kq_{e}q_{p}}{d^{2}} \)

Where:

K: is the Coulomb's constant = 9x10⁹ N.m²/C²      

\(q_{p}\): is the charge of the proton = 1.6x10⁻¹⁹ C

\(q_{e}\): is the charge of the electron = -1.6x10⁻¹⁹ C

d: is the distance = 5.3x10⁻¹¹ m

Hence, the magnitude of the electric force is:

\( |F_{e}| = \frac{9\cdot 10^{9} N.m^{2}/C^{2}*(-1.6\cdot 10^{-19} C)*1.6 \cdot 10^{-19} C}{(5.3 \cdot 10^{-11} m)^{2}} = 8.20 \cdot 10^{-8} N \)                

2. The gravitational force can be calculated as follows:

\( F_{g} = \frac{Gm_{e}m_{p}}{d^{2}} \)

Where:

\(m_{e}\): is the electron's mass = 9.1x10⁻³¹ kg

\(m_{p}\): is the proton's mass = 1.67x10⁻²⁷ kg

G: is the gravitational constant = 6.67x10⁻¹¹ N.m²/kg²

Therefore, the gravitational force is:

\( F_{g} = \frac{6.67 \cdot 10^{-11} N.m^{2}/kg^{2}*9.1 \cdot 10^{-31} kg*1.67 \cdot 10^{-27} kg}{(5.3 \cdot 10^{-11} m)^{2}} = 3.61 \cdot 10^{-47} N \)

As we can see, the gravitational force is much less than the electric force.

I hope it helps you!                                                      

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Explanation:

0.4 = 4/10 = 2/5

The original slope as a fraction is 2/5

Flip the fraction to get 5/2, then flip the sign to get -5/2 which is the perpendicular slope

The orginal slope 2/5 and perpendicular slope -5/2 multiply to -1. This is true of any pair of perpendicular lines where neither line is vertical nor horizontal.

Rephrased another way: -5/2 is the negative reciprocal of 2/5.

\(y = {x}^{2} + 4x - 12\)

The exponential function, considering the base e, can be written as follows:

\(f(t) = 8000e^{0.02t}\)

The standard definition of an exponential function is given as follows:

\(A(t) = A(0)\left(1 + \frac{r}{n}\right)^{\frac{t}{n}}\).

The parameters are given as follows:

The function for this problem is given as follows:

\(f(t) = 5000(1.4)^{\frac{t}{20}}\)

Considering the base e, the rate of change is obtained as follows:

k = 0.4/20 = 0.02.

Hence the function is written as follows:

\(f(t) = 8000e^{0.02t}\)

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Answer:

They charge the same

Step-by-step explanation:

i hope this helps

The 96% confidence interval for the fraction of the voting population favoring the annexation suit is approximately 0.493 to 0.647.

To find the 96% confidence interval for the fraction of the voting population favoring the suit, we can use the formula for a confidence interval for a proportion.

The formula for a confidence interval for a proportion is given by:

P ± z * √(P(1-P)/n)

where P is the sample proportion, z is the z-score corresponding to the desired confidence level, √ represents the square root, and n is the sample size.

In this case, the sample proportion is P = 114/200 = 0.57 (since 114 out of 200 voters support the suit).

The z-score corresponding to a 96% confidence level can be obtained using a standard normal distribution table or calculator. For a two-tailed test, the z-score is approximately 1.750.

The sample size is n = 200.

Now we can substitute these values into the formula:

P ± z * √(P(1-P)/n)

0.57 ± 1.750 * √((0.57 * (1 - 0.57))/200)

Calculating the values:

√((0.57 * (1 - 0.57))/200) ≈ 0.045

0.57 ± 1.750 * 0.045

Calculating the confidence interval:

Lower bound: 0.57 - 1.750 * 0.045 ≈ 0.493

Upper bound: 0.57 + 1.750 * 0.045 ≈ 0.647

Therefore, the 96% confidence interval for the fraction of the voting population favoring the annexation suit is approximately 0.493 to 0.647.

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Incomplete question:

A random sample of 200 voters is selected and 114 are found to support an annexation suit. Find the 96% confidence interval for the fraction of the voting population favoring the suit.

Answer:

v=pi.r^2.h

1728=3.14*22r^2

1728/69.08=r^2

r^2=25.0144

r=5

The Solution:

Given:

Required:

Find the inverse of the given function.

Step 1:

Let:

Step 2:

Isolate x.

Step 3:

Replace y with x.

Answer:

[option D]

Answer:

120

Step-by-step explanation:

1/3 = 40

3/3= 40 x3

    =120

Answer:

There are as many odd numbers as there are natural numbers.

Step-by-step explanation:

Answer:

18.84, 75.36, 169.56, and 301.44

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

A simple way to solve this is by substituting, we start with trying 1 for x, 2+6=8, and 1+9=10. Because the two values are different, that means 1 is the incorrect value. We can try 2, 4+6=10, and 2+9=11, once again inequivalent. We finally try 3, and 6+6=12 and 3+9=12 meaning x must be 3

Answer:

x=75

Step-by-step explanation:

∆FSJ~∆DYJ

so the sides are proportional

SJ/YJ=FJ/DJ

(63+42)/42=(x+50)/50

105/42 ×50=x+50

125-50=x

x=75

Answer:

X=75

Step-by-step explanation:

FD/DJ=SJ/YJ=FS/DY(BEING CORESSPONDING SIDE OF SIMILAR TRAINGLES)

TAKING FIRST AND SECOND RATIO

OR X/50=63/42

OR X*42=63*50

OR X=3150/42

OR X=75

Answer:

v=-2

Step-by-step explanation:

if v = -2, 8 x -2= -16

To solve this problem, we have to use the equivalence of each type in dollars.

Taking x, y and z as the number of nickels, dimes and quarters, we have that:

0.05 is the equivalence of one nickel in dollars, same for 0.1 and 0.25 with dimes and quarters respectively.

Now, we know that she has 2 more dimes than nickels:

And 4 more quarters than nickels:

We can use the expression for y and z in terms of x in the first equation to find the value of x (number of nickels):

Once we have found x, we can use it to find y and z using the equations we stated:

It means that Susan has 3 nickels, 5 dimes and 7 quarters.

1. The radius of the sphere is \(\(\sqrt{21}\)\).

2. The distance from the center of the sphere to the xz-plane is 1.

1. To find the radius of the sphere with diameter AB, we can use the distance formula. The distance between two points in 3D space is given by:

\(\[d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2}\]\)

Using the coordinates of points A and B, we can calculate the distance between them:

\(\[d = \sqrt{(-6 - 2)^2 + (2 - 0)^2 + (1 - (-3))^2} = \sqrt{64 + 4 + 16} = \sqrt{84}\]\)

Since the diameter of the sphere is equal to the distance between A and B, the radius of the sphere is half of that distance:

\(\[r = \frac{1}{2} \sqrt{84} = \frac{\sqrt{84}}{2} = \frac{2\sqrt{21}}{2} = \sqrt{21}\]\)

2. To find the distance from the center of the sphere to the xz-plane, we need to find the z-coordinate of the center. The center of the sphere lies on the line segment AB, which is the line connecting the two points A and B.

The z-coordinate of the center can be found by taking the average of the z-coordinates of A and B:

\(\[z_{\text{center}} = \frac{z_A + z_B}{2} = \frac{-3 + 1}{2} = -1\]\)

Therefore, the distance from the center of the sphere to the xz-plane is the absolute value of the z-coordinate of the center, which is |-1| = 1.

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Answer:

1.08

Step-by-step explanation:

Find the number in the hundredth place

8

and look one place to the right for the rounding digit

3

. Round up if this number is greater than or equal to

5

and round down if it is less than

5

.

A firm experiences increasing returns to scale if inputs are doubled and output more than doubles.

When the firm's output grows at a faster rate than the growth in inputs, increasing returns to scale result. In this case, the company experiences economies of scale, which makes it more effective as it grows its production.

The firm is able to boost productivity and efficiency as it expands its scale of operations if inputs are doubled and output more than doubles.

This can be ascribed to a number of things, including specialisation, labour division, the use of capital-intensive technology, discounts for bulk purchases, and spreading fixed costs over a higher output. Lower average costs per unit of output result in higher profitability and competitiveness for the company.

The firm gains a number of benefits from growing returns to scale. First off, it lets the company to benefit from cost savings brought about by economies of scale, allowing it to manufacture goods or services for less money per unit. This may enable more competitive pricing on the market or result in larger profit margins.

Second, raising returns to scale can result in better operational effectiveness and resource utilisation. As the company grows in size, it will be able to use resources more wisely and profit from production volume-related synergies.market prices that are competitive.

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#1

m<LOM=m<JKL

#2

Linear pair .

#3.

Complementary angles

#4

Angle bisector theorem

#5

Similarity theorem

As per the given condition m ∠LOM = m ∠JKI, m ∠MON = m ∠IKH it is proved that m ∠LON = m ∠HKJ as they are congruent angles.

"Congruent angles is defined as the angles with equal measure."

According to the question,

In the given figure of the angles,

m ∠LOM = m ∠JKI  (given congruent angles)                     _____(1)

m ∠MON = m ∠IKH  (given congruent angles)                  _______(2)

Add both the side angle  m ∠MON in (1) we get ,

m ∠LOM + m ∠MON = m ∠JKI + m ∠MON

Replace angle  m ∠MON = m ∠IKH from (2)  on right hand side we get,

m ∠LOM + m ∠MON = m ∠JKI + m ∠IKH      ____(3)

m ∠LOM + m ∠MON = m ∠LON  ( M is the interior point of ∠LON)    ___(4)

m ∠JKI + m ∠IKH = m ∠HKJ  ( I is the interior point of ∠HKJ)            ___(5)

Form (3) , (4) and (5) we get,

m ∠LON = m ∠HKJ  (Congruent angles)

Hence, form the given condition it is proved that m ∠LON = m ∠HKJ , are congruent angles.

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Answer:

y=3x+15

Step-by-step explanation:

she can make 3 a day so 3x and she already has 15 so the line crosses the y-axis  at 15

Calculating the area of a triangle:

\(A=\frac{1}{2}bh\)

1. determine base and height measurements

2. apply the formula

\(A=\frac{1}{2}(12m)(8m)\\\)

\(A = 48m^2\)

95% confidence level means there are chances that the true mileage improvement of Arco Graphite motor oil lies within the range of 1% to 8.7% compared to conventional motor oil.

In the context of the advertisement for Arco Graphite motor oil,

The phrase 95% confidence level means that the tests conducted to measure the mileage improvement of the Arco Graphite motor oil.

Compared to conventional motor oil were performed with a 95% level of confidence.

Stated differently, if the same tests were conducted multiple times.

There is a 95% probability that the true average mileage improvement of Arco Graphite motor oil would fall within the range of 1% to 8.7% .

As compared to conventional motor oil.

The remaining 5% represents the possibility that the true average mileage improvement of Arco Graphite motor oil falls outside this range.

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Answer:

28.4 degrees

Step-by-step explanation:

sin(theta) = 20/42. theta=arcsin(10/21)=28.43

It will take approximately 138 months or 11 years and 6 months for the tithe to double in value if invested at 7.75% APR compounded monthly.

To solve this problem, we can use the Time Value of Money (TVM) Solver function in Excel or a financial calculator.

The TVM Solver helps to calculate the time required to double the initial amount invested, given the interest rate, compounding frequency, and the present value of the investment.

Using the TVM Solver, we can enter the following values:

Number of Periods (N) = the time required to double the initial investment

Solving for N, we get:

N = 138.24 months

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Number of side of polygon will be 18.

What is polygon?

A plane figure may be a figure that's delineated by a finite variety of line segments connected to create a closed plane figure chain is called polygon.

Main body:

Since the sum of the exterior angles of a polygon is 360° and an angle of the regular polygon is 20°, then 360° / 20° is the number of sides. Let the number of sides be n.

n = 18, an octadecagon.

Measure of Each Interior Angle

If you imagine a regular octadecagon (or any polygon), you will notice that the exterior angle is the supplement of the interior angle.

20° = 180° - I, where I is the interior angle.

[20°] + I = [180° -I] + I

[20° + I] - 20° = [180°] - 20°

I = 160 degrees

Sum of the Interior Angles:

Sum of interior angles is 180° (n - 2). The way I remember this equation is by remembering that the equation contains 180° and the number of sides, and that the sum of interior angles of a triangle is 180°.

=180° (18 - 2)

=180° (16)

=(200 - 20)° (16)

=(3200 - 320)°

=2880°

Sum of the Exterior and Interior angles

360° + 2880° = 3240°

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Answer:

10.5

Step-by-step explanation:

Break the problem down into small parts:

2 to the power of 3= 8

8+7+6=

15+6=21

21/2

21 divided by 2 is 10.5

Hope this helps!

The length of side BC, |BC|, is 2 units. The correct option is C. 2 units

From the question, we are to determine the length of side BC

First, we will determine the length of side BD

From Pythagorean theorem, we can write that

|BD|² = |AB|² + |AD|²

From the given information,

|AB| = 1

|AD| = 1

Thus,

|BD|² = 1² + 1²

|BD|² = 1 + 1

|BD|² = 2

|BD| = √2

Also, we can write that

|BC|² = |BD|² + |DC|²

From the given information,

|BD| = |DC|

Thus,

|BC|² = (√2)² + (√2)²

|BC|² = 2 + 2

|BC|² = 4

|BC| = √4

|BC| = 2

Hence, side BC is 2 units

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a) U is subspace of R^3.

b) The set {(3, -2, 0), (0, 1/2, 1)} is a basis for U.

c) 2.

a) To show that U is a subspace of R^3, we need to verify the following three conditions:

i) The zero vector (0, 0, 0) is in U.

ii) U is closed under addition.

iii) U is closed under scalar multiplication.

i) The zero vector is in U since 0 + 2(0) - 3(0) = 0.

ii) Let (x1, y1, z1) and (x2, y2, z2) be two vectors in U. Then we have:

x1 + 2y1 - 3z1 = 0 (by definition of U)

x2 + 2y2 - 3z2 = 0 (by definition of U)

Adding these two equations, we get:

(x1 + x2) + 2(y1 + y2) - 3(z1 + z2) = 0

which shows that the sum (x1 + x2, y1 + y2, z1 + z2) is also in U. Therefore, U is closed under addition.

iii) Let (x, y, z) be a vector in U, and let c be a scalar. Then we have:

x + 2y - 3z = 0 (by definition of U)

Multiplying both sides of this equation by c, we get:

cx + 2cy - 3cz = 0

which shows that the vector (cx, cy, cz) is also in U. Therefore, U is closed under scalar multiplication.

Since U satisfies all three conditions, it is a subspace of R^3.

b) To find a basis for U, we can start by setting z = t (where t is an arbitrary parameter), and then solving for x and y in terms of t. From the equation x + 2y - 3z = 0, we have:

x = 3z - 2y

y = (x - 3z)/2

Substituting z = t into these equations, we get:

x = 3t - 2y

y = (x - 3t)/2

Now, we can express any vector in U as a linear combination of two vectors of the form (3, -2, 0) and (0, 1/2, 1), since:

(x, y, z) = x(3, -2, 0) + y(0, 1/2, 1) = (3x, -2x + (1/2)y, y + z)

Therefore, the set {(3, -2, 0), (0, 1/2, 1)} is a basis for U.

c) Since the basis for U has two elements, the dimension of U is 2.

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Answer:

1, -3, 9, -27, (81),-243,729,-2187

Step-by-step explanation:

81 is the answer

Answer:

81, - 243, 729

Step-by-step explanation:

There is a common ratio between consecutive terms in the sequence, that is

r = - 3 ÷ 1 = 9 ÷ - 3 = - 27 ÷ 9 = - 3

Thus to obtain a term in the sequence multiply the previous term by - 3

- 27 × - 3 = 81

81 × - 3 = - 243

- 243 × - 3 = 729