a test charge of 1µc is placed halfway between a charge of 3.2µc and another of 8.2 µc separated by 10 cm. what is the magnitude of the force (in newtons) on the test charge?

The area of the base of the pyramid is 35/4 m².

The volume of the pyramid is 14 m³.

A pyramid is a three-dimensional geometric shape that has a base and triangular sides that meet at a common point, called the apex.

The formula for the area of the base of the pyramid is given as:

A = 1/2 bh

where b and h are the base and height of the triangle at the base of the pyramid.

Given b = 7/3 meters and h = 15/2 meters

A = 1/2 * 7/3 * 15/2

A = 35/4 m²

That is B = 35/4 m²

The formula for the volume of the pyramid is given as:

V = 1/3 Bh

where h is the height of the pyramid and h = 24/5 meters

V = 1/3* 35/4 * 24/5

V = 14 m³

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An exponential function would better approximate the data described about the volume of a gas.

The relationship between the volume of a gas and its temperature is described by the Ideal Gas Law, which states that the volume of a gas is proportional to its temperature raised to the power of the ratio of specific heat to the universal gas constant. Therefore, as the temperature of a gas increases, its volume will increase exponentially.

The data given in the problem, with the volume increasing as the temperature increases, supports the use of an exponential function to model the relationship between temperature and volume. On the other hand, a linear function, which models a constant rate of change, would not accurately capture the exponential increase in volume as the temperature increases.

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Answer:

1. x = 20

2. m<ABK = 137

Step-by-step explanation:

1.

(3x - 5) + (4x + 2) + (2x + 3) = 180

9x  = 180

x = 20

2.

3x - 5 + 4x + 2

7x - 3

7(20) - 3

140 - 3

m<ABK = 137

Answer:

79.4cm

Step-by-step explanation:

1cm = 10mm so 794mm / 10mm = 79.4cm

Assuming that interest for a given month is based on the balance for the previous month, it will take 6 months to pay off the credit card debt of $1,200 when making a net payment of $225.

An online finance calculator can determine the period for a compound interest system.

The length of payment uses the beginning credit card balance of $1,200 and the net payment of $225 (since a monthly payment of $300 is made when an additional charge of $75 is withdrawn from the card).

I/Y (Interest per year) = 18%

PV (Present Value) = $1,200

PMT (Periodic Payment) = $-225 ($300 - $75)

FV (Future Value) = $0

Results:

Period (N #) = 5.6

Sum of all periodic payments = $-1,260.08

Total Interest = $60.08

Thus, within six months you can pay off the credit card debt.

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If you divide 63 by 3 you get 21.

If you divide 42 by 2 you get 21.

63 / 3 = 21

42 / 2 = 21

Therefore, the GCF(Greatest Common Factor)is 21.

Answer:

1:3:5

Step-by-step explanation:

[tex]\frac{7}{7}=1\\\\\frac{21}{7}=3\\ \\\frac{35}{7}=5[/tex]

1:3:5

The table which represents a linear relationship that is also proportional is table 1.

There is a linear relationship between y and x when the rate of change of y with respect to x will be equal.

Table 1:

xy

00

42

84

When x = 4

y = kx

2 = k×4

2 = 4k

k = 2/4

k = 0.5

y = kx

y = 0.5x

when x = 8

y = 0.5(8)

y = 4

Table 2:

xy

01

23

45

y = kx

when x = 2

3 = k × 2

3 = 2k

k = 3/2

k = 1.5

when x = 4

y = 1.5x

y = 1.5(4)

y = 6

Therefore, table 1 is proportional and represents a linear relationship with the equation y = 0.5x.

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The probability of having n-1 failures before the first success in a Geometric distribution, given a specific probability p.

The formula (1-p)n-1 represents the probability of having n-1 failures (or successes, depending on which outcome the probability p is associated with) in a Geometric distribution. For example, if p=0.3, then the formula (1-p)n-1 would represent the probability of having two failures before the first success. This would be equal to (1-0.3)2-1, or 0.49. This means that there is a 49% chance of having two failures before the first success in this example. In general, this formula can be used to calculate the probability of having n-1 failures before the first success in a Geometric distribution, given a specific probability p.

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Complete question:

What does (1-p)n-1 represent in a geometric distribution?

Answer:

Step-by-step explanation:

2

BECUASE YEA

Answer:

Step-by-step explanation:

h(x) = -x + 1

h(x) = 0

0 = -x + 1

-1 = -x

x = 1

Answer: 324/4

Step-by-step explanation:

I know i'm doing this totally wrong I don't know.

The probability of selecting a spade and then selecting a heart is 0.0625, and the correct answer is option A.

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.

Given that the cards are selected with replacement.

The probability of selecting a spade card is:

P(S) =13/52

Now, a heart card is selected.

Since, the previous card is replaced in the deck the total number of cards is 52.

The probability of selecting a heart card is:

P(H) = 13/ 52

The probability of selecting a spade and then selecting a heart is:

P = 13 / 52 × 13/52

P = 0.0625

Hence, the probability of selecting a spade and then selecting a heart is 0.0625, and the correct answer is option A.

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Answer:

Below

Step-by-step explanation:

5 out of 8 are NOT blue     5/8=.625

The relationship the ratios of sin x° and cos y° share is The ratios are both identical (five thirteenths and five thirteenths). Option B

Trigonometric Identities are defined as the qualities involving trigonometry functions and also holds true for all the values of the variables given in the equation.

The different types of trigonometric identities are given as;

From the information given, we have that

sin = opposite/hypotenuse

cos = adjacent/hypotenuse

But;

Hypotenuse= 13

Opposite = 5

Adjacent = 12

Substitute the value

sin x = 5/13

cos y = 5/13

Hence, the values are identical

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Answer:

B!

Step-by-step explanation:

took the testt

Length of the diagonal of the rectangular prism is 14.69694. Here is the solution below

Given that the information:

Length of the rectangular prism - 10

Width of the rectangular prism - 4

Height of the rectangular prism - 10

Length of the diagonal of the rectangular prism -

Diagonal (d) = √l²+w²+h²= √10²+4²+10² =  14.69694

A rectangular prism is a three-dimensional shape, that has six faces (two at the top and bottom and four are lateral faces). All the faces of the prism are rectangular in shape. Hence, there are three pairs of identical faces here. Due to its shape, a rectangular prism is also called a cuboid.

The correct answer of this question is 14.69

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Answer:

28

Step-by-step explanation:

The slope of a line represents the rate of change between two variables. In the case of Superior Segway Tours, the cost of the tour is changing as the number of hours for the tour changes. The rate of change can be calculated by dividing the change in the dependent variable (cost) by the change in the independent variable (hours). In this case, the slope is $28 per hour. This means that for every hour that is added to the tour, the cost will increase by $28.

The slope of this situation can be represented as the change in cost (y-axis) per unit change in time (x-axis). The slope in this case would be $28 per hour.

You and your friend are approximately 181.23 meters apart at that point in time.

To find the distance between you and your friend, we can use the Pythagorean theorem. Let's call the distance between you two "d".

d² = 250² + 195² - 2 X 250 X 195 X cos(18)

d = √(250² + 195² - 2 X 250 × 195 X cos(18))

d ≈ 181.23 m

So you and your friend are approximately 181.23 meters apart.

The answer was determined using the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two smaller sides equals the square of the length of the largest side (the hypotenuse).

In this case, the two smaller sides represent the distances covered by you and your friend, and the hypotenuse represents the distance between you both.

We can use the theorem to calculate the distance "d" between you and your friend by rearranging the equation to isolate "d". We know the lengths of the two smaller sides (250 m and 195 m), and we also know the angle between them (18 degrees).

We can use the cosine formula to find the cosine of 18 degrees, and plug in all the values into the equation to find "d".

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Answer: The inverse of the function k(x)=x²-3 is k^(-1)(x)=±√(x+3). The domain restrictions for the inverse are x≥-3, since the square root is only defined for non-negative values.

The inverse of a function is the reflection of the original function over the line y=x. To find the inverse of k(x)=x²-3, we first swap the x and y variables: y=x²-3. Then, we solve for x: x=±√(y+3). This gives us the inverse function k^(-1)(x)=±√(x+3).

However, it is important to note that the square root function is only defined for non-negative values. Therefore, we must restrict the domain of the inverse function to x≥-3. This means that the inverse function can only be applied to input values that are greater than or equal to -3. For values less than -3, the inverse function is undefined.

Step-by-step explanation:

Answer:

Inverse function: [tex]\pm \sqrt{x + 3}[/tex]

Domain: [tex]x \ge -3[/tex]

Step-by-step explanation:

[tex]k(x) = x^2-3[/tex]

To find the inverse, set y = k(x)

==> y = x² - 3

Swap x and y

x = y² - 3

Add 3 to both sides
x + 3 = y²

y² = x + 3

[tex]y = \pm \sqrt{x + 3}[/tex]

or, in other words:

[tex]y = \sqrt{x +3} \:\;and\; y = -\sqrt{x + 3}[/tex] are the two solutions

Replace Swap x and y again to get the inverse as a function of x
[tex]k^{-1}(x) = \sqrt{x+3},\:-\sqrt{x+3}[/tex]

Since square roots of negative numbers are not defined, the term under the square root must be ≥ 0

x + 3 ≥ 0

==> x ≥ -3

There is no restriction on the upper bound it can go upto infinity

Domain of [tex]\sqrt{x + 3} : \:x\ge \:-3[/tex]

After maxing x as a subject the solution becomes: x = z³ + √d 3a. This can be solved using the concept of solving equation.

Equations simultaneously, or a system of equations Multiple equations in algebra must be solved simultaneously. There must be an equal number of equations and unknowns for a system to have a singular solution. When two or more equations use the same variables, they are said to be in a system of equations. Graphing, substitution, and elimination are the three techniques used to solve systems of equations.

For instance, two equations with the identical variables, x and y, are x + y = 12 and 2x + 5y = 8. They are an equalization system.

Given that,

[tex]\sqrt{d} =\frac{ x - z^3}{3a}[/tex]

or, x - z³ = √d 3a

or, x = z³ + √d 3a

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B and C

Right pyramid has 8, Right triangular prism has 9

Using the cosine ratio, the measure of angle A, to the nearest hundredth is: 75.52°.

The cosine ratio, also known simply as the cosine, is a trigonometric function that represents the ratio of the adjacent side to the hypotenuse of a right triangle.

It is defined as cos(θ) = adjacent side/hypotenuse, where θ is the angle between the adjacent side and the hypotenuse.

Reference angle (∅) = A

Length of adjacent side = 2

Length of hypotenuse = 8

Therefore:

cos A = adj./hyp. = 2/8

cos A = 1/4

A = cos^(-1)(1/4)

A = 75.52°

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Answer

Y=-2x+1

-2 is the slope, and 1 is the y intercept

In a triangle ABC, angle B=90, angle C=60, angle A=30 and BC=12cm. The area of the triangle is 144 * (√3/2) sq cm

In a right triangle with a 90 degree angle, the length of the side opposite the 90 degree angle is the height, and the length of the other two sides form the base. If angle C = 60 degrees, then angle A = 90 - 60 = 30 degrees.

If BC = 12 cm, then the height AC is equal to AB * sin(30) = 12 * (√3/2).

The area of the triangle is equal to (1/2) * base * height = (1/2) * 12 * (12 * (√3/2)) = (12 * 12 * (√3/2))/2 = 144 * (√3/2) sq cm

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The complete question goes thus:

In a triangle ABC, angle B=90, angle C=60, angle A=30 and BC=12cm. What is the area of the triangle?

54.10Answer:

Step-by-step explanation:

The numerical length of PQ is 20

A line segment in geometry is a section of a line that has two clearly defined endpoints and contains every point on the line that lies within its confines.

Given that the line segments are: -

OQ=11  O P = 9

The numerical value of PQ will be calculated as below.

OP+OQ=PQ

11+9=PQ=11+9=PQ

Therefore PQ=20=PQ

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The student will need to save approximately 488.33 dollars per month in order to pay off the remaining cost at the end of 12 months.

First, let's calculate the amount that the student's grandparent will pay: 19,700 / 2 = 9,850

Next, let's subtract the amount of the athletic scholarship: 19,700 - 9,850 - 5,000 = 5,850

Finally, to find the minimum amount that the student will need to save every month, we can divide the remaining cost by the number of months (12): 5,850 / 12 = 488.33

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The number of zeros of the polynomial p(x) is 3.

A polynomial is a mathematical expression that solely uses the addition, subtraction, and multiplication operations to combine variables (commonly called coefficients) and variables (often called x). The variables are raised to non-zero, and the coefficients can be any real value.

The number of x-intercepts, or the places where the graph crosses the x-axis, is equal to the number of polynomial roots, also known as zeros.

We can see from the above graph that the polynomial p(x) has three x-intercepts, which indicates that it has three roots or zeros. Consequently, the polynomial p(x) has three zeros.

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Complete question -

Elimination.... my biggest enemy

Welp let's dive in.

Elimination is sort of like subtraction BUT it's subtraction of equations.

In Elimination we want to make sure that we are looking for a common/ opposite coefficient.

If we see 5x and 5x stacked on each other, GREAT! or maybe -5x and 5x stacked on each other.

Why am I happy? Welll that just made the whole process easier. You see, if you see those stacked on top of each other, that means free elimation. You can just cancel them out because it becomes zero.

then we solve the problem same old same old.

P.S: If it's opposites coefficients we add the equations if it's the same we subract.

In your elimination, we have the same coefficients.

(yay)

so we can minus ad and ad

6c with 5c and 111 with 103

c=8

so we pick an equation and sustitute every c with 8

6*8+ad=111

48+ad=111

ad=63

questiojns? feel free to ask

On a principal of $100,000.00 with compound interest accrued at a rate of 7% per year compounded continuously over 4 years, the total sum is $132,312.98.

The interest earned on savings that are computed using both the original principal and the interest accrued over time is known as compound interest. A = P(1 + r/n)^nt, where P is the principal balance, r is the interest rate, n is the number of times interest is compounded annually, and t is the number of years, which is the formula for compound interest.

Given,  You have an inheritance of $100,000 from your grandparents, you must invest the money in a mutual fund until you are 21 years old, which will pay an annual interest rate of r% compounded continuously.

From the general formula of compound interest:

A = Pe^rt,

where P is the principal balance,

r is the interest rate,

n is the number of times interest is compounded annually,

t is the number of years

In our case,

P = 100,000

t = 21 - 17 = 4

n = 12 for compounded continuously

thus,

A = 100,000(2.71828)^r4

For the value of r = 7

A = 100,000.00(2.71828)^(0.07)(4)

A = $132,312.98

Therefore, The total amount accrued, principal plus interest, with compound interest on a principal of $100,000.00 at a rate of 7% per year compounded continuously over 4 years is $132,312.98.

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