How would I categorize numbers? For example, what category would √23 fit into? Thankssss

Equation

C = (F - 32) ÷ 1.8

Solution

C = (112 - 32) ÷ 1.8

=44.4  (44.4444444444)

Answer may vary depending on how your teacher wants you to do it and whether they want a exact answer.

On September 15, Jerome, Incorporated purchased debt investments as trading securities at a cost of $8,850.

The journal entry for this transaction would include the following accounts: "Debt Investments" and "Cash." Since Jerome, Incorporated purchased debt investments as trading securities, the "Debt Investments" account will be debited to record the increase in the asset. The "Cash" account will be credited to reflect the outflow of cash due to the purchase.

The journal entry would be as follows:

Date: September 15

Account Debit ($) Credit ($)

Debt Investments 8,850

Cash 8,850

By debiting the "Debt Investments" account, we increase the value of the investment on the company's balance sheet. The corresponding credit to the "Cash" account shows the decrease in cash resulting from the purchase. This journal entry accurately records the acquisition of debt investments as trading securities by Jerome, Incorporated on September 15.

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Answer:

k = 56

Step-by-step explanation:

2k + 68 = 180

2k = 112

112 ÷ 2 = 56

k = 56

Answer:

28.

Step-by-step explanation:

b + 19 =

(9) + 19 =

9 + 19 = 28

Answer:

28

Step-by-step explanation:

Substitute b with 9 so it's 19 + 9 = 28

Have a great day <3

Perpendicularity law

Answer:

Add it all up and then divide by the amount of sides there are

Hints your answer will be 5.7 (5cm) rounded

Step-by-step explanation:

I hope this helps you :)

-KeairaDickson

Answer:

2p < 7

Step-by-step explanation:

Two p which is 2p is less than or fewer than 7. No equal to so no line under it.

The inequality 2p < 7 represents the word sentence "Twice a number p is fewer than 7" and indicates that the value of p must be less than 3.5.

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

The word sentence "Twice a number p is fewer than 7" can be written as the inequality:

2p < 7

In this inequality, "2p" represents twice the value of the number p, and "7" represents the value that twice the number p is fewer than.

To explain further, if we divide both sides of the inequality by 2, we get:

p < 3.5

This means that the value of p is less than 3.5. So, any number that is less than half of 7 (which is equal to 3.5) satisfies the inequality.

Therefore, the inequality 2p < 7 represents the word sentence "Twice a number p is fewer than 7" and indicates that the value of p must be less than 3.5.

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To find the cubic function f(x) given the conditions f(5) = 100, f(-5) = f(0) = f(6) = 0, we need to solve the system of linear equations formed by substituting the values into the general cubic function f(x) = ax^3 + bx^2 + cx + d. Once the values of a, b, and c are determined, the formula for f(x) can be expressed as f(x) = ax^3 + bx^2 + cx.

To find a formula for a cubic function f(x) given the conditions f(5) = 100, f(-5) = f(0) = f(6) = 0, we can start by assuming that the cubic function takes the form f(x) = ax^3 + bx^2 + cx + d.

Using the given conditions, we can create a system of equations to solve for the coefficients a, b, c, and d:

1. f(5) = 100: 100 = a(5)^3 + b(5)^2 + c(5) + d

2. f(-5) = 0: 0 = a(-5)^3 + b(-5)^2 + c(-5) + d

3. f(0) = 0: 0 = a(0)^3 + b(0)^2 + c(0) + d

4. f(6) = 0: 0 = a(6)^3 + b(6)^2 + c(6) + d

Simplifying these equations, we get:

1. 100 = 125a + 25b + 5c + d

2. 0 = -125a + 25b - 5c + d

3. 0 = d

4. 0 = 216a + 36b + 6c + d

From equation 3, we find that d = 0. Substituting this value into equations 1, 2, and 4, we have:

1. 100 = 125a + 25b + 5c

2. 0 = -125a + 25b - 5c

4. 0 = 216a + 36b + 6c

We can solve this system of linear equations to find the values of a, b, and c. Once we have those values, we can express the formula for f(x) as f(x) = ax^3 + bx^2 + cx + d, where d is already determined to be 0.

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The most appropriate graphical representation for the grams of fiber from 1,000 different breakfast cereals sold in the United States is; Histogram, because there is a large set of data.

Since histogram is a graphical representation of the distribution of numerical data. This is consist of a series of adjacent rectangles, or bins, that are used to represent the frequency distribution of the data. The height of each bin corresponds to the number of data points that fall within a particular range or interval.

Hence, we have that each bin will represent the number of observations in an interval of grams of fiber.

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Answer:

I'm pretty sure 8 is the correct answer

Step-by-step explanation:

(-1)^(3/7)  x 128^(3/7)

-1 x 128^3/7

128^(3/7) = 8

= 8

Therefore, on average, Martin will not win or lose any money using this gambling strategy. The expected net winnings are $0.

To determine the average amount of money Martin will win using the given gambling strategy, we can consider the possible outcomes and their probabilities.

Let's analyze the strategy step by step:

On the first toss, Martin bets $1 on Heads.

If he wins, he earns $1 and stops.

If he loses, he moves to the next step.

On the second toss, Martin bets $2 on Heads.

If he wins, he earns $2 and stops.

If he loses, he moves to the next step.

On the third toss, Martin bets $4 on Heads.

If he wins, he earns $4 and stops.

If he loses, he moves to the next step.

And so on, continuing to double the bet until Martin wins or reaches the limit of his available money ($31 in this case).

It's important to note that the probability of winning a single toss is 0.5 since the coin is fair.

Let's calculate the expected value at each step:

Expected value after the first toss: (0.5 * $1) + (0.5 * -$1) = $0.

Expected value after the second toss: (0.5 * $2) + (0.5 * -$2) = $0.

Expected value after the third toss: (0.5 * $4) + (0.5 * -$4) = $0.

From the pattern, we can see that the expected value at each step is $0.

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The coordinates of the preimage triangle ABC are A = (1.5,3.75),  B = (3,0), and  C = (5,3.75)

From the question, we have the following parameters that can be used in our computation:

A′(6,15), B′(12,0), and C′(20,15)

Scale factor = 4

The above points represent the image after the triangle has been dilated

Mathematically, this can be represented as

A′B′C′ = ABC * Scale factor

Substitute the known values in the above equation, so, we have the following representation

A′(6,15), B′(12,0), and C′(20,15) = ABC * 4

Divide both sides of the equation by 4

So, we have the following representation

1/4 * A′(6,15), B′(12,0), and C′(20,15) = ABC * 4 * 1/4

Evaluate the quotients

So, we have the following representation

A(1.5,3.75), B(3,0), and C(5,3.75) = ABC

This means that

A = (1.5,3.75),  B = (3,0), and  C = (5,3.75)

Hence, the coordinates of the preimage are A = (1.5,3.75),  B = (3,0), and  C = (5,3.75)

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Answer:

The Median is 75

Step-by-step explanation:

median is the middle number in a set of given numbers

arranging in order will be

30,64,70,80,90,110

the middle numbers are 70 and 80

Median=80+70/2

=150/2

Median=75

Using the monthly payment formula, it is found that her down payment should be of $1,419.

It is given by:

\(A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}\)

In which:

For this problem, the parameters are:

A = 250, r = 0.072, n = 72.

Hence:

r/12 = 0.072/12 = 0.006.

We solve for P to find the total amount of the monthly payments, hence:

\(A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}\)

\(P\frac{0.006(1.006)^{72}}{(1.006)^{72}-1} = 250\)

0.0171452057P = 250

P = 250/0.0171452057

P = $14,581.

The total payment is of $16,000, hence her down payment should be of:

16000 - 14581 = $1,419.

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Answer: D:22,

14,040-12,500=1540.  

1540/70 = 22

The inner product of two vectors A = (2, -3,0) and B = (-1,0,5) is -2 / √(13×26).

Solving the given system of equations using Gaussian elimination:

2x + 3y + z = 2 y + 5z = 20 -x+2y+3z = 13

Matrix form of the system is

[A] = [B] 2 3 1 | 2 0 5 | 20 -1 2 3 | 13

Divide row 1 by 2 and replace row 1 by the new row 1: 1 3/2 1/2 | 1

Divide row 2 by 5 and replace row 2 by the new row 2: 0 1 1 | 4

Divide row 3 by -1 and replace row 3 by the new row 3: 0 0 1 | 5

Back substitution, replace z = 5 into second equation to solve for y, y + 5(5) = 20 y = -5

Back substitution, replace z = 5 and y = -5 into the first equation to solve for x, 2x + 3(-5) + 5 = 2 2x - 15 + 5 = 2 2x = 12 x = 6

The solution is (x,y,z) = (6,-5,5)

Therefore, the solution to the given system of equations using Gaussian elimination is (x,y,z) = (6,-5,5).

The given two vectors are A = (2, -3,0) and B = = (-1,0,5). The inner product of two vectors A and B is given by

A·B = |A||B|cosθ

Given,A = (2, -3,0) and B = (-1,0,5)

Magnitude of A is |A| = √(2²+(-3)²+0²) = √13

Magnitude of B is |B| = √((-1)²+0²+5²) = √26

Dot product of A and B is A·B = 2(-1) + (-3)(0) + 0(5) = -2

Cosine of the angle between A and B is

cosθ = A·B / (|A||B|)

cosθ = -2 / (√13×√26)

cosθ = -2 / √(13×26)

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Answer: After 20 laps Paula will have more money than Jackie.

Step-by-step explanation:

Let x = Number of laps.

Given, Paula has $10 and earns $0.50 per lap she runs for her school’s fundraiser.

i.e. Total amount Paula has =$ [ 10 +0.50 (Number of laps)]

= $ [10+0.50x]

Jackie has $15 and earns $0.25 per lap she runs for her school’s fundraiser.

i.e. Total amount Jackie has =$ [ 15 +0.25 (Number of laps)]

= $ [15+0.25x]

When Paula has more money , then

\(15+0.25x< 10+0.50x\\\\\Rightarrow\ 15-10<0.50x-0.25x\\\\\Rightarrow\ 5< 0.25x\\\\\Rightarrow\ \dfrac{5}{0.25}<x\\\\\Rightarrow\ 20<x\)

Hence, after 20 laps Paula will have more money than Jackie.

Answer: 4 Chocolates

When r = 5 and q = -4, the value of P is 23.

The value of P when r = 5 and q = -4, we can simply substitute these values into the equation P = 7r + 3q and perform the arithmetic:

P = 7(5) + 3(-4)

P = 35 - 12

P = 23

An equation is a statement that asserts the equality of two mathematical expressions, which are typically composed of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. An equation can be used to represent a wide range of mathematical relationships, from simple arithmetic problems to complex functions and systems of equations.

Equations are often used to model and solve problems in various fields of science, engineering, and economics, among others. For example, the laws of physics can be expressed through equations, such as the famous E=mc² equation that relates energy and mass in Einstein's theory of relativity. Equations can also be used to model economic relationships, such as supply and demand curves, or to solve engineering problems, such as the stress and strain of a material under load.

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1.1) The volume of the cube is 27 cubic centimeters. 1.2)the density of the ice cube is approximately 0.917 grams per cubic centimeter (g/cm³).

1.3) the mass of the water cube is 27 grams. 1.4) the weight of the water and the ice would be the same under the same conditions. 1.5)In simpler terms, ice floats on water because it is lighter (less dense) than the water, allowing it to displace an amount of water equal to its weight and float on the surface.

1.1) The volume of the cube can be calculated using the equation: Volume = width x height x length. In this case, the cube measures 3 cm wide, 3 cm tall, and 3 cm long, so the volume is:

Volume = 3 cm x 3 cm x 3 cm = 27 cm³.

Therefore, the volume of the cube is 27 cubic centimeters.

1.2) Density is defined as mass divided by volume. The mass of the ice cube is given as 24.76 grams, and we already determined the volume to be 27 cm³. Therefore, the density of the ice cube is:

Density = Mass / Volume = 24.76 g / 27 cm³ ≈ 0.917 g/cm³.

Therefore, the density of the ice cube is approximately 0.917 grams per cubic centimeter (g/cm³).

1.3) The volume of the water cube is the same as the ice cube, which is 27 cm³. Given the density of liquid water as 1.00 g/cm³, we can calculate the mass of the water cube using the equation:

Mass = Density x Volume = 1.00 g/cm³ x 27 cm³ = 27 grams.

Therefore, the mass of the water cube is 27 grams.

1.4) The weight of an object depends on both its mass and the acceleration due to gravity. Since the volume of the water cube and the ice cube is the same (27 cm³), and the mass of the water cube (27 grams) is equal to the mass of the ice cube (24.76 grams), their weights would also be equal when measured in the same gravitational field.

Therefore, the weight of the water and the ice would be the same under the same conditions.

1.5) Ice floats on water because it is less dense than liquid water. The density of ice is lower than the density of water because the water molecules in the solid ice are arranged in a specific lattice structure with open spaces. This arrangement causes ice to have a lower density compared to liquid water, where the molecules are closer together.

When ice is placed in water, the denser water molecules exert an upward buoyant force on the less dense ice, causing it to float. The buoyant force is the result of the pressure difference between the top and bottom surfaces of the submerged object.

In simpler terms, ice floats on water because it is lighter (less dense) than the water, allowing it to displace an amount of water equal to its weight and float on the surface.

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Answer:

20

Step-by-step explanation:

dekameter=10 meters

dekameter*2

20 meters

20/20=1

20 meter long pieces

Answer:2

Step-by-step explanation:

The specific values of \($\underline{-33.78}$\) and \($\overline{-33.78}$\) depend on the level of precision required.

The upper and lower bounds for -33.78 depend on the level of precision required. For example, if we only need to round to the nearest whole number, the lower bound is -34 and the upper bound is $-33$. If we need to round to the nearest tenth, the lower bound is -33.8 and the upper bound is -33.7.

In general, we can use the following notation to indicate the upper and lower bounds of a number x:

\($$\underline{x} \leq x \leq \overline{x}$$\)

Using this notation, we can write the upper and lower bounds for -33.78 as:

\($$\underline{-33.78} \leq -33.78 \leq \overline{-33.78}$$\)

Again, the specific values of \($\underline{-33.78}$\) and \($\overline{-33.78}$\) depend on the level of precision required.

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Answer:

60

Step-by-step explanation:

If there are 300 calories in 100g of Bill's food, then we can divide 5 on both  sides to find the number of calories in a 20g portion of this food: 300/5=60 calories.

Answer: (1, -1)

Step-by-step explanation:

you would first start out with

5x+2y=3

4x-8y=12

you would then subsitute the value of x

x=3/5-2/5 y

4x-8y=12

you then solve the equation

4(3/5-2/5 y) -8y=12

you then subsitute the vaulue of y

y=-1

then you solve the equation

x=3/5-2/5 x(-1)

A possile solution is

x=1

you should then check the solution

(x,y) = (1,-1)

Answer:

The rate of change is also called the slope.  The slope is -2

Step-by-step explanation:

Find 2 points on the line.  I am going to use the points (0,5) and (4, -3).  the rate is the change in y over the change in x.  From the two points, my values are -3 and 5.  The x values are 4 and 0.

To find the change, I subtract the y values and the x values.

\(\frac{-3-5}{4-0}\) = \(\frac{-8}{4}\) = -2

Answer: -2

Step-by-step explanation: The rate of change is also known as the slope!

To find the slope, you need to find the rise/run.

Let's pick two points ( 0,5) ( 4, -3)

You see that the y goes down by 8 and the x goes right by 4, so the rate of change is -8/4 = -2

If you can, please give me a Brainliest; thank you!

Answer:

\(\huge\boxed{Slope = 3}\)

Step-by-step explanation:

The coordinates are (5,6) and (6,9)

Slope = Rise / run

Slope = \(\frac{y2-y1}{x2-x1}\)

Slope = \(\frac{9-6}{6-5}\)

Slope = \(\frac{3}{1}\)

Slope = 3

Answer:

\(slope = 3\)

Hope this helps you

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Answer:

Width = 7 units

Step-by-step explanation:

Width = x

Length = 3x + 1

2x + 2(3x+1) = 58

2x + 6x + 2 = 58

8x = 58-2

x = 56/8

x = 7

Main Answer:

c₁ = 2, c₂ = 4, a₁ = 6, a₂ = 0, b₁ = 0, b₂ = 0.

Explanation:

In the given problem, we are provided with a periodic signal x(t) and we need to determine the coefficients c₁, c₂, a₁, a₂, b₁, and b₂ using the given Fourier series representation.

Step 1: Find c₁ and c₂:

c₁ is the coefficient of cos(wo₁t) in x(t), and c₂ is the coefficient of cos(wo₂t) in x(t). In the given signal x(t) = 2cos(5t) + 4cos(15t) + 6sin(20t), we can see that there is no term of the form cos(wo₁t) or cos(wo₂t). Therefore, c₁ and c₂ both equal 0.

Step 2: Find a₁ and a₂:

a₁ is the coefficient of cos(wo₁t) in x(t), and a₂ is the coefficient of cos(wo₂t) in x(t). We can calculate these coefficients using the formula:

an = (2/T) * ∫[0 to T] x(t) * cos(nwot) dt

For the given signal x(t) = 2cos(5t) + 4cos(15t) + 6sin(20t), we have:

a₁ = (2/1) * ∫[0 to 1] (2cos(5t) + 4cos(15t) + 6sin(20t)) * cos(wo₁t) dt

  = (2/1) * ∫[0 to 1] (2cos(5t)) * cos(wo₁t) dt

  = (2/1) * ∫[0 to 1] (2cos(5t)) * cos(5t) dt

  = (2/1) * ∫[0 to 1] (2cos²(5t)) dt

  = (2/1) * [∫[0 to 1] cos²(5t) dt]

  = (2/1) * [∫[0 to 1] (1 + cos(10t))/2 dt]

  = (2/1) * [(t/2) + (sin(10t))/(20)] (evaluated from 0 to 1)

  = 1/2 + sin(10)/(10)

Similarly, a₂ = 0 as there is no term of the form cos(wo₂t) in the given signal.

Step 3: Find b₁ and b₂:

b₁ is the coefficient of sin(wo₁t) in x(t), and b₂ is the coefficient of sin(wo₂t) in x(t). We can calculate these coefficients using the formula:

bn = (2/T) * ∫[0 to T] x(t) * sin(nwot) dt

For the given signal x(t) = 2cos(5t) + 4cos(15t) + 6sin(20t), we have:

b₁ = (2/1) * ∫[0 to 1] (2cos(5t) + 4cos(15t) + 6sin(20t)) * sin(wo₁t) dt

  = (2/1) * ∫[0 to 1] (6sin(20t)) * sin(5t) dt

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