What are the real and imaginary parts of the complex number?

-6-i

Jim answered 30 out of 35 questions correctly, which is 85.7% correct when calculated using the percentage formula.

Jim got 30 questions correct out of a total of 35. To find the percentage of questions he got correct, you can use the formula for calculating percentages: Percentage = (Number of correct answers ÷ Total number of questions) × 100%. Applying this formula to Jim's case: Percentage = (30 ÷ 35) × 100% = 0.857 × 100% = 85.7%. Therefore, Jim got 85.7% of the questions correct.

The distance between the points R (-1,1) and S (-4,-5) is [tex]3\sqrt{5}[/tex] units.

To find the distance between points R(-1, 1) and S(-4, -5), we can use the distance formula in a coordinate plane.

The distance formula is given by:

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

Using the given coordinates:

[tex]x_1 = -1, y_1 = 1[/tex](coordinates of point R)

[tex]x_2 = -4, y_2 = -5[/tex] (coordinates of point S)

[tex]d = \sqrt{(-4 +1 )^2 + (-5 - 1)^2}[/tex]

[tex]d = \sqrt{9 +36}[/tex]

[tex]d = \sqrt{45}[/tex]

[tex]d = \sqrt{9 \times 5}[/tex]

[tex]d = 3\sqrt{5}[/tex]

Hence, the distance between the points R (-1,1) and S (-4,-5) is [tex]d = 3\sqrt{5}[/tex] units.

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Answer:

the correct answer is B.-2/3

Final answer:

The incorrect statement is that the nucleus of an atom contains protons and electrons; actually, the nucleus contains protons and neutrons, with electrons orbiting around it.

Explanation:

The statement that does not correctly describe the structure of an atom is 'Inside the nucleus of an atom are protons and electrons'. This statement is incorrect because the nucleus of an atom actually contains protons and neutrons, not electrons. Electrons are negatively charged sub-atomic particles that orbit around the nucleus. The nucleus itself is a small, dense center that is positively charged due to the presence of protons, which are positively charged. Neutrons, which have no electric charge, are also found within the nucleus.

Further expanding on atomic structure, the nucleus is very tiny compared to the rest of the atom, which is mostly empty space. The electrons residing in this space are in perpetual motion, creating a cloud-like region around the nucleus. Despite their small mass compared to protons and neutrons, the number of electrons equals the number of protons in a neutral atom, balancing the charge.

To graph the solution set of the inequality 15x + 10y ≥ 1100, find the intercepts of the graph and draw a line passing through them. Then, test a point not on the line to determine which side represents the solution set. The solution set of the inequality is the region below the line on the graph.

To graph the solution set of the inequality 15x + 10y ≥ 1100, we can start by identifying the intercepts of the graph. An intercept is a point where the graph intersects either the x-axis or the y-axis. To find the x-intercept, we set y = 0 in the inequality: 15x + 10(0) ≥ 1100. Simplifying this equation, we have 15x ≥ 1100. Dividing both sides by 15, we get x ≥ 73.33. Therefore, the x-intercept is (73.33, 0).

To find the y-intercept, we set x = 0 in the inequality: 15(0) + 10y ≥ 1100. Simplifying this equation, we have 10y ≥ 1100. Dividing both sides by 10, we get y ≥ 110. Therefore, the y-intercept is (0, 110).

After finding the intercepts, we can draw a line passing through these two points. Since the inequality is ≥, the line will be solid (including the points on the line). Finally, we determine which side of the line represents the solution set. We can choose a test point not on the line, such as (0, 0), and substitute its coordinates into the inequality. If the inequality is true, the shaded region representing the solution set should be below the line.

If the inequality is false, the shaded region should be above the line. In this case, substituting (0, 0) into the inequality gives 15(0) + 10(0) = 0, which is less than 1100. Therefore, the shaded region should be below the line. The solution set of the inequality 15x + 10y ≥ 1100 is the region below the line on the graph.

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The height of the rain barrel is required.

The height of the barrel is 2.39 feet.

r = Radius of barrel = 2 feet

V = Volume of barrel = 30 cubic feet

h = Height of barrel

Since, the barrel is cylindrical the volume of the barrel is

[tex]V=\pi r^2h\\\Rightarrow h=\dfrac{V}{\pi r^2}\\\Rightarrow h=\dfrac{30}{3.14\times 2^2}\\\Rightarrow h=2.3885\approx 2.39\ \text{feet}[/tex]

The height of the barrel is 2.39 feet.

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Answer:

Combine like terms

Subtraction property of inequality

Division property of inequality

Step-by-step explanation:

We are given tnat

[tex]75x+35\geq 7(11x+9)+4[/tex]

We have to find the missing justification in given solution

[tex]75x+35\geq 7(11x+9)+4[/tex]

Reason:Given

[tex]75x+35\geq 77x+73+4[/tex]

Reason:Distributive property

[tex]75x+35\geq 77x+67[/tex]

Reason:combine ike terms

[tex]-2x+35\geq 67[/tex]

Reason:Subtraction property of order

[tex]-2x\geq 32[/tex]

Reason:Subtraction property of inequality

[tex]x\leq -16[/tex]

Reason:Division property of inequality

Answer:

ASA  and AAS

Step-by-step explanation:

We do not know if these are right triangles; therefore we cannot use HL to prove congruence.

We do not have 2 or 3 sides marked congruent; therefore we cannot use SSS or SAS to prove congruence.

We are given that EF is parallel to HJ.  This makes EJ a transversal.  This also means that ∠HJG and ∠GEF are alternate interior angles and are therefore congruent.  We also know that ∠EGF and ∠HGJ are vertical angles and are congruent.  This gives us two angles and a non-included side, which is the AAS congruence theorem.

Since EF and HJ are parallel and EJ is a transversal, ∠JHG and ∠EFG are alternate interior angles and are congruent.  Again we have that ∠EGF and ∠HGJ are vertical angles and are congruent; this gives us two angles and an included side, which is the ASA congruence theorem.

Answer: ASA  and AAS

Step-by-step explanation:

length of AC = 10 * sin(30) = 5 cm

Length of CD = 5 /tan(25) = 10.7cm

 answer is C

Answer

Find out the what is the length of CD , AC .

To prove

By using the trignometric identity

[tex]sin B = \frac{Perpendicular}{Hypotenuse}[/tex]

As in ΔABC

∠ B = 30° , AB= 10 cm

put in the trignometric identity

[tex]sin 30^{\circ} = \frac{AC}{10}[/tex]

As

[tex]sin30^{\circ} =\frac{1}{2}[/tex]

[tex]\frac{1}{2} = \frac{AC}{10}[/tex]

[tex]AC = \frac{10}{2}[/tex]

AC = 5cm

Now in the ΔADC

[tex]tan D^{\circ} = \frac{Perpendicular}{Base}[/tex]

∠ D = 25° , AC = Perpendicular = 5 cm

[tex]tan 25^{\circ} = \frac{5}{CD}[/tex]

tan 25 ° =  0.46630765815 (approx)

[tex]CD = \frac{5}{0.46630765815}[/tex]

CD = 10 .7cm ( approx )

Option (C) is correct .

Answer:

The answer is C, 40

Answer: D.24 - 2d

Step-by-step explanation: I took the test Hope you have a good day. PEACE

the average value of f(x) = 1/x over the interval [e, 2e] is, ln(2)/e.

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.

here, we have,

f(x) = 1/x over the interval [e, 2e].

i.e. we get,

[tex]\frac{1}{2e-e}[/tex] × [tex]\int\limits^{2e}_e {1/x} \, dx[/tex] =1/e. ln (x)[2e, e]

                        =ln(2e)/e - ln(e)/e

                        =[ln2+lne/e] - 1/e

                        =ln2/e +1/e -1/e

                        =ln(2)/e

hence,  the average value of f(x) = 1/x over the interval [e, 2e] is, ln(2)/e.

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Answer:

The average rate of change of a function f(x) in the first two seconds is 25.

Step-by-step explanation:

Given : Graph , X represent the time , function f(x).

To find : the average rate of change of a function f(x) in the first two seconds is____.

Solution : The rate of change of f(x) with respect to x is the slope of the line.

slope : [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex].

In first two second  ( 0, 50 ) , ( 2, 100).

slope : [tex]\frac{100-50}{2-0}[/tex].

slope : [tex]\frac{50}{2 }[/tex].

the average rate of change of a function f(x) in the first two seconds is 25.

Therefore,The average rate of change of a function f(x) in the first two seconds is 25.

Answer:

The correct option is A= 1/8 B= 5/16 C= 7/12 D= 5/6

Step-by-step explanation:

Consider the provided fractions.

First convert each fraction into decimal form as shown:

5/6 = 0.833..

7/12 = 0.5833..

1/8 = 0.125

5/16 = 0.3125

The largest number among them is 0.833.. i.e 5/6 and the smallest number among them is 0.125 i.e 1/8

Arrange them in increasing order as shown:

0.125, 0.3125, 0.5833.., 0.833.. or 1/8, 5/16, 7/12, 5/6

Now consider the provided figure. The alphabets are showing the number are in increasing order

Thus, the correct option is A= 1/8 B= 5/16 C= 7/12 D= 5/6

Answer:

40 Miles.

5 hrs.

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2

Janet has to pay off $65 to reduce her balance to no more than $60.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that Janet has a balance of 125 on a credit card on her next statement she wants to reduce her balance to no more than 60.

The amount to be paid will be calculated as,

Amount = 125 - 60

Amount = $65

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The ages of James, Paul and Dan is required.

James is 30 years old, Paul is 80 years old and Dan is 10 years old.

Let the ages of James be [tex]j[/tex], Paul be [tex]p[/tex] and Dan be [tex]j[/tex].

James is three times the age of Dan

[tex]j=3d[/tex]

Paul is two times the sum of the ages of James and Dan

[tex]p=2(j+d)\\\Rightarrow p=2(3d+d)\\\Rightarrow p=2(4d)=8d[/tex]

The combined ages of the people is 120

[tex]j+p+d=3d+8d+d\\\Rightarrow 120=12d\\\Rightarrow d=\dfrac{120}{12}\\\Rightarrow d=10[/tex]

[tex]j=3d=3\times 10\\\Rightarrow j=30[/tex]

[tex]p=8d=8\times 10\\\Rightarrow p=80[/tex]

So, James is 30 years old, Paul is 80 years old and Dan is 10 years old.

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A fair coin is flipped six times. Then 1/22  is the probability that heads occurs exactly 4 times if it is known that heads occurs at least four times

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event.

The probability that heads occurs exactly 6 times if it is known that heads occurs at least four times is

P{H=6|H≥4}

= P{(H=6)∩(H≥4)}/P{H≥4}

= P{H=6}/P{H≥4}      

We need to calculate P{H=6}

P{H=6} = C(6,6)(½)6

= (½)6

P{H≥4} = P{H=4} + P{H=5} + P{H=6}

= C(6,4)(½)4(½)2 + C(6,5)(½)5(½) + C(6,6)(½)6

= (½)6[C(6,4) + C(6,5) + C(6,6)]

= (½)6[15 + 6 + 1]

= (½)6(22)

Therefore,

P{H=6|H≥4} = 1/22

1/22  is the probability that heads occurs exactly 4 times if it is known that heads occurs at least four times

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Part A: Alligators: [tex]\(A(t) = 20 \times (1 + 0.25)^t\), Crocodiles: \(C(t) = 25 + 10t\).[/tex]

Part B: After 4 years: Alligators: ~38, Crocodiles: 65.

Part C: Alligators and crocodiles equal: Solve [tex]\(20 \times (1 + 0.25)^t = 25 + 10t\).[/tex]

Part A:

Let's define the functions to represent the number of alligators and crocodiles in the swamp over the years.

For alligators:

[tex]\[A(t) = A_0 \times (1 + r)^t\][/tex]

Where:

[tex]- \(A(t)\) is the number of alligators in the swamp after \(t\) years.\\- \(A_0\) is the initial number of alligators (20 in this case).\\- \(r\) is the growth rate per year (25% or 0.25).\\- \(t\) is the number of years.[/tex]

For crocodiles:

[tex]\[C(t) = C_0 + n \times t\][/tex]

Where:

[tex]- \(C(t)\) is the number of crocodiles in the swamp after \(t\) years.\\- \(C_0\) is the initial number of crocodiles (25 in this case).\\- \(n\) is the number of new crocodiles joining each year (10 in this case).\\- \(t\) is the number of years.[/tex]

Part B:

To find the number of alligators after 4 years, we use the formula:

[tex]\[A(4) = 20 \times (1 + 0.25)^4\][/tex]

To find the number of crocodiles after 4 years, we use the formula:

[tex]\[C(4) = 25 + 10 \times 4\][/tex]

Part C:

To find when the number of alligators and crocodiles are the same, we set [tex]\(A(t) = C(t)\) and solve for \(t\).[/tex]

[tex]\[20 \times (1 + 0.25)^t = 25 + 10 \times t\][/tex]

This equation can be solved numerically to find the value of \(t\) when the number of alligators and crocodiles are the same.

To solve this problem, we simply have to use ratio and proportion.

We know that 15 gallons is consumed in 10 minutes therefore the conversion factor is:

15 gallons / 10 minutes

Therefore in 77 minutes:

water consumed = (15 gallons / 10 minutes) * 77 minutes

water consumed = 115.5 gallons

Answer:

i need the equation I know that the distance is 105 miles

Step-by-step explanation:

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