A Man And A Woman Receive A Monthly Salary Of Gh3725 And Gh2962 Respectively. Find Their Total Income (2024)

The first ship with an angle of depression 9° has a 2399.23m distance from the shore. And the first and second ship are on a 1944.19m distance apart.

What is an angle of depression

The angle of depression is an angle formed between the horizontal line and the line of sight when an observer looks downwards.

Considering the right triangle formed by the height of the cliff and the distance of the ships from the shore, we shall derive a complementary angle considering their respective angles of depression as:

90° - 9° = 81° for the first ship

90° - 5° = 85° for the second ship

such that;

tan 81° = distance of the first ship from the shore/380m {opposite/adjacent}

distance of the first ship from the shore = 380m × cos 81°

distance of the first ship from the shore = 2399.23m

tan 85° = distance of the second ship from the shore/380m {opposite/adjacent}

distance of the second ship from the shore = 380m × cos 85°

distance of the second ship from the shore = 4343.42

the ships distance apart = 4343.42m - 2399.23m

the ships distance apart = 1944.19m

Therefore, first ship with an angle of depression 9° has a 2399.23m distance from the shore. And the first and second ship are on a 1944.19m distance apart.

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Answer: The discount is $13.75, which is found by multiplying the original price by the discount percentage, 0.25.

Step-by-step explanation:

Erik’s average speed in miles per hour is 114. 04 miles per hour

What is average speed?

Average speed can simply be defined as the total distance that is traveled by the object in a particular time range.

It is also known as a scalar quantity, that is, it has magnitude but no direction.

From the information given, we have that;

Distance = 2623 milesTime taken = 23 hours

The formula for average speed is expressed as;

Average speed = Distance/ time

Substitute the values, we get;

Average speed = 2623/23

Divide the values, we get;

Average speed = 114. 04 miles per hour

Hence, the value is 114. 04 miles per hour

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Answer:

All the answers are bolded in the step-by-step explanation.

Hope it helps :)

Step-by-step explanation:

The radius of the top of a cylinder is always the same length as the radius of the base of a cylinder.

Radius of the base of can A: 10 cm

Radius of the base of can B: 18 cm

To find the area of the bases, use the area formula that you put as your first answer.

Area of the base of can A:

[tex]A=\pi (10^{2} )[/tex]

[tex]A=100\pi[/tex]

[tex]A=314[/tex] cm (Assuming we're only using 3.14 and not any other decimals)

Area of the base of can B:

[tex]A=\pi (18^{2} )[/tex]

[tex]A=324\pi[/tex]

[tex]A=1017.36[/tex] cm (Again, assuming we're only using 3.14 and not any other decimals)

The base of can B has a greater Area

To find the height, look at the diagram

Height of can A: 28cm

Height of can B: 9cm

Can A has a greater height

To find the volume, use the equation that you put as your answer for question 2 or just multiply the area of the base times the height.

Volume of can A:

[tex]314*28=V[/tex]

[tex]V=8792[/tex]

Volume of can B:

[tex]1017.36*9=V[/tex]

[tex]V=9156.24[/tex]

Can B holds more paint

When we take a marble from the bag, the number of red marbles decreases by 1 and the total number of marbles decreases by 1 as well.

So after the first draw, the probability of getting a red marble on the second draw becomes 4/7 (since there are now 4 red marbles out of 7 total marbles).

To find the probability of getting 2 red marbles in a row, we multiply the individual probabilities of getting a red marble on each draw:

P(2 red marbles) = P(red marble on first draw) * P(red marble on second draw)

P(2 red marbles) = (5/8) * (4/7) = 20/56 = 5/14

So the probability of getting 2 red marbles in a row is 5/14.

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Answer: 18

Step-by-step explanation: Solve using algebra and angles given.

The solution of the equations y = - 2x + 17 and y = x - 7 will be (8, 1). Then the correct option is D.

What is a linear equation?

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The linear equations are given below.

y = - 2x + 17 ...1

y = x - 7 ...2

From equations 1 and 2, then we have

x - 7 = - 2x + 17

3x = 24

x = 8

Then the value of 'y' is given as,

y = 8 - 7

y = 1

The solution of the equations y = - 2x + 17 and y = x - 7 will be (8, 1). Then the correct option is D.

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In linear equation, 80 cups of water will yonni need to replace all the water in the fish tank.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Now, as we know:

1 quart = 0.25 gallons

⇒ 4 pints = 1 gallons

⇒ 8 pints = 2 gallons

Also, 1 pint = 0.5 quart

⇒ 2 pints = 1 quarts

⇒ 8 pints = 4 quarts

⇒ 16 pints = 8 quarts

Again, 1 cup = 0.5 pint

⇒ 2 cup = 1 pint

⇒ 32 cup = 16 pints

so 16 * 5 = 80 cups

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Answer:

6 days

Step-by-step explanation:

This is an easy problem if you think about it. Let’s start by identifying unnecessary information. I’ll go ahead and point this out: we don’t need to know how long it takes Johnny to watch the episodes. The question already says he’s only watching 12 episodes per day, so the time information is useless. If you rewrite the problem with only message information, you get something like this:

“The show Johnny wants to binge watch is 61 episodes long. If Johnny were to watch 12 episodes a day, how many days would it take him to finish the show?”

That makes it seem so much easier! Let’s start by dividing the show into sets of 12 episodes. 61 divided by 12 is 5 R1. Since he needs another day to finish the show, even if he only watches one episode, the answer is 6 days.

So there are ten different combinations of two pupils out of five when there are five kids in my class and I want to choose two to treat to lunch.

What is combination?

A combination in mathematics is a selection of elements from a set with distinct members, where the order of selection is irrelevant. A combination is a mathematical approach for determining the number of potential arrangements in a set of objects when the order of the selection is irrelevant. You can choose the components in any order in combinations. Permutations and combinations are often mistaken. A combination is a method of picking elements from a collection when the order of selection is irrelevant. Assume we have three integers P, Q, and R. Combination defines how many possibilities we may choose two numbers from each set.

Here,

To determine the number of ways to pick 2 students out of 5 to treat them to lunch, you can use the combination formula, which is given by nCr, where n is the number of items to choose from, r is the number of items to choose, and nCr is the number of combinations of n items taken r at a time. In this case, n = 5 and r = 2, so the number of ways to pick 2 students out of 5 is:

5C2 = 5! / (2! * (5 - 2)!) = 10

So, there are 10 possible combinations of 2 students out of 5 when there are 5 students in my class and I want to pick 2 to treat them to a lunch.

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Answer:0.625

Step-by-step explanation:

Answer:

0.615, 0.609, 0.516, 0.506

Answer:

204000$ is the new selling price

I think

Answer:

2040000

Step-by-step explanation:

15%of 240 000 is 36 000

240 000 - 36 000 = 204000

A measure of central tendency is a single data that represents the center spot of a dataset. This data can also be known as “the central location” of a dataset.

In statistics, there are mainly three common measures of central tendency:

1. The mean is: (41 + 44 + 99 + 46 + 39 + 47 + 38 + 46) / 8 = 46

2. The median is:

38, 39, 41, 44, 46, 46, 47, 99

Middle values: 44 and 46

Average of middle values: (44 + 46) / 2 = 45

The median of this data set is 45.

3. In this case, the mode is 46, as it appears twice in the data set.

All of these measures find the central location of a dataset using various methods. Depending on the type of data you are analyzing, one of these three measures may be better to use than the other two.

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15% of the students scored higher than Henry on the accounting exam.

What is percentiles?

Percentiles are a measure of the relative standing of a value within a set of values. The nth percentile is a value such that n% of the values are less than or equal to that value.

So, if Henry's score is in the 85th percentile, it means that 85% of the scores in the class are less than or equal to his score.

Therefore, 100% - 85% = 15% of the scores in the class are higher than Henry's score. So, 15% of the students scored higher than Henry on the accounting exam.

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Answer:

7 miles

Step-by-step explanation:

Let's call the distance from point C to point D as "x".

We know that the distance from A to B is 8 miles, and the distance from A to D is 4 miles. To ensure that all three towers are equidistant from each other, the distance from C to B must be equal to 8 miles.

Using the Pythagorean Theorem, we can find the distance from C to D:

(x)^2 + (4)^2 = (8)^2

Expanding and simplifying the equation:

x^2 + 16 = 64

x^2 = 48

x = sqrt(48) = 6.928

So the distance from the third tower to point D is approximately 6.9 miles (rounded to the nearest tenth of a mile).

Answer:

6.9 miles

Step-by-step explanation:

Since the distance between points A and B is 8 miles, and point C is equidistant from points A and B, triangle ABC is an equilateral triangle with side lengths of 8 miles.

As point D is 4 miles from point A, point D is the midpoint of AB.

Therefore, the distance between point C and point D is the altitude of the triangle.

The formula for the altitude of an equilateral triangle is:

[tex]h=\dfrac{\sqrt{3}}{2}s[/tex]

where s is the the side length.

Therefore, the altitude of an equilateral triangle with side length 8 miles is:

[tex]\implies h=\dfrac{\sqrt{3}}{2} \cdot 8[/tex]

[tex]\implies h=4\sqrt{3}[/tex]

[tex]\implies h=6.9\; \sf miles\;(nearest\;tenth)[/tex]

Therefore, the distance from the third tower C to point D is 6.9 miles to the nearest tenth of a mile.

The solution of the piecewise function at the given values of the independent variable g(0) is 5, g(-7) is 12 and g(2) is 7.

This is an example of a piecewise function, which is a function composed of two or more parts, each part being defined by a separate equation.

In this function, the first part is defined as g(x) = x+5 if x >= -5, and the second part is defined as g(x) = -(x+5) if x < -5.

To evaluate the function at the given values of the independent variable, we can simply substitute the values into the appropriate equation.

At x = 0,

=> g(0) = 0+5 = 5.

At x = -7,

=> g(-7) = -(-7+5) = 12.

And at x = 2,

=> g(2) = 2+5 = 7.

Therefore, the values of the function are 5, 12, and 7 respectively

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Answer: To happen before

Step-by-step explanation:

Answer:

this equation is always true

Step-by-step explanation:

Solve the equation and check your solution: -2(x - 1) = 2 - 2x

-2(x - 1) = 2 - 2x

-2x + 2 = 2 - 2x

-2x + 2x = 2 - 2

0 = 0

(this equation is always true)

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

check

whatever value you give to x the equation is always true, let's take 2 as an example

-2(2-1) = 2 - 2 * 2

-4 + 2 = 2 - 4

-2 = -2

The value of a geometric sequence can not be zero, because for that we have to include 0 as a term in it and that will turn the sequence into zero.

What is geometric sequence?

A geometric progression, also known as a geometric sequence, is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.

In geometric sequences, the terms given by the ratio of every two successive terms is a constant. they can be either negative or positive but not zero, because if any term will be zero it will directly make the common ratio equal to 0, that will make the sequence turning to 0, and it won't be a geometric progression anymore, therefore, the successive values of a geometric sequence could become infinitesimally small but never be equal to 0.

An example of a Geometric sequence is 2, 4, 8, 16, 32, 64, …, where the common ratio is 2.

If suppose 2nd term is 0, then common ratio = 0/2 = 0, that will disturb the pattern and the sequence will not be a GP

Hence, the successive values of a geometric sequence could become infinitesimally small but never be equal to 0.

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The fraction of the area of the triangle that would be shaded in stage 7 is equal to 2,187/16,384.

No, there isn't a stage when the fraction of area shaded would be equal to 0.

What is a fraction?

In Mathematics, a fraction simply refers to a numerical quantity which is not expressed as a whole number. This ultimately implies that, a fraction is simply a part of a whole number.

Next, we would determine the area of the triangle that would be shaded in stage 2 is as follows;

Fraction of the area = 3/4 × 3/4 = 9/16.

The area of the triangle that would be shaded in stage 3 is as follows;

Fraction of the area = 3/4 × 3/4 × 3/4 = 27/64.

The area of the triangle that would be shaded in stage 4 is as follows;

Fraction of the area = 3/4 × 3/4 × 3/4 × 3/4 = 81/256.

Therefore, the area of the triangle that would be shaded in stage 7 is as follows;

Fraction of the area = 3/4 × 3/4 × 3/4 × 3/4 × 3/4 × 3/4 × 3/4 = 2,187/16,384.

In this context, we can reasonably infer and logically deduce that there isn't a stage when the fraction of area shaded in this triangle would be equal to zero (0) because there is a linear relationship between the shaded and unshaded area.

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The value of balance after 6 years compounded quarterly is , $44,450

What is Simple interest?

A quick and easy method of calculating the interest charge on a loan is called a Simple interest.

Given that;

You deposit 35000 in an account that pays 2.3% annual interest.

We know that;

Amount = P (1 + r/4)⁴ⁿ

Where, P is the starting amount, r is interest rate and n is time.

Substitute all the value we get;

Amount = P (1 + r/4)⁴ⁿ

Amount = 35000 (1 + 0.023/4)²⁴

Amount = 35000 (4.023/4)²⁴

Amount = 35000 × 1.01²⁴

Amount = 35000 × 1.27

Amount = $44,450

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Answer:

Step-by-step explanation:

No, the number of students at Lake View Middle School is not proportional to the number of teachers.

Proportionality between two quantities means that they maintain a constant ratio, regardless of their actual values. In this case, if the number of students and teachers were proportional, we would expect the ratio of students to teachers to remain constant as the total number of students or teachers changes.

However, in this scenario, the ratio of students to teachers is not constant. The ratio is 48:2, which simplifies to 24:1. This means that there are 24 students for every 1 teacher. If the number of students at the school were to double to 96, we would expect the number of teachers to double as well if they were proportional. However, this would mean that there would be 4 teachers assigned to the students, which is twice the original number of teachers assigned to the original number of students.

Therefore, the number of students at Lake View Middle School is not proportional to the number of teachers, because the ratio of students to teachers is not constant, and it changes as the total number of students or teachers changes.

The correlation coefficient measures the strength of the linear relationship between two variables. A coefficient of 0.8 implies a strong linear relationship between two variables, a coefficient of 0.25 implies a weak linear relationship between two variables.

0.8: Strong Association

0.25: Weak Association

0.9: Strong Association

0.65: Moderate Association

The correlation coefficient is a numerical measure of the strength of the linear relationship between two variables. Values of the correlation coefficient fall between -1 and +1. A coefficient of 0 implies that there is no linear relationship between two variables. The closer the coefficient is to either -1 or +1, the stronger the correlation. A coefficient of 0.8 implies a strong linear relationship between two variables, a coefficient of 0.25 implies a weak linear relationship between two variables, a coefficient of 0.9 implies a very strong linear relationship between two variables, and a coefficient of 0.65 implies a moderate linear relationship between two variables.

The correlation coefficient measures the strength of the linear relationship between two variables. A coefficient of 0.8 implies a strong linear relationship between two variables, a coefficient of 0.25 implies a weak linear relationship between two variables, a coefficient of 0.9 implies a very strong linear relationship between two variables, and a coefficient of 0.65 implies a moderate linear relationship between two variables.

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well, we know angle θ is in the III Quadrant, that means the sine or opposite side and cosine or adjacent side are both negative, whilst of course the hypotenuse is just a radius amount thus is always positive.

[tex]\sin(\theta )=\cfrac{\stackrel{opposite}{-3}}{\underset{hypotenuse}{4}}\hspace{5em}\textit{let's find the \underline{adjacent side}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2 - b^2}=a ~~ \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \pm\sqrt{4^2 - (-3)^2}=a \\\\\\ \pm\sqrt{7}=a\implies \stackrel{III~Quadrant}{-\sqrt{7}=a}\hspace{5em} \boxed{\cos(\theta )=\cfrac{\stackrel{adjacent}{-\sqrt{7}}}{\underset{hypotenuse}{4}}}[/tex]

No, AA Criterion should not be called the AAA Criterion, because we need only two angles to be equal to prove the similarity.

What is AA criterion?

According to the AA triangle similarity criterion, two triangles are considered similar if their three angles are identical to one another. Equi-angular triangles are comparable in a nutshell.

Since just two pairs of angles must be equal in order for the third pair to be automatically equal thanks to the angle sum property of triangles, the proper term for this criterion would then be the AAA(Angle-Angle-Angle) criterion. However, we refer to it as the AA criterion instead.

Hence, no, because we need only two angles to be equal to prove the similarity.

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Answer:

450

Step-by-step explanation:

the speed of mass is 450

The distance of the probe is given by the equation A = 2.546 light years

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

The distance traveled by the space probe = 1.7 light years

Now , the value of 1 light year = 9.461 x 10¹³

So , the distance traveled by the space probe = 1.7 x value of 1 light year

On simplifying the equation , we get

The distance traveled by the space probe D = 1.7 x 9.461 x 10¹³

The distance traveled by the space probe D = 16.0837 x 10¹³ km

The distance traveled by the space probe D = 1.60837 x 10¹⁴ km

The distance to Proxima Centauri = 4.246 light years

So , the remaining distance is A = distance to Proxima Centauri - distance traveled by the space probe

On simplifying the equation , we get

The remaining distance is A = 2.546 light years

Hence , the equation is A = 2.546 light years

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the voltage across the circuit ([tex]V_{0}[/tex]) is 80 volts.

In the superposition theorem, the voltage across any element in a linear circuit is equal to the sum of the voltages caused by each source acting independently. In other words, in a linear circuit, each source is treated as the only source, and the other sources are replaced with their internal resistances.

With the resistance value of 8 ohms, we can calculate the voltage across the circuit using the superposition theorem.

First, consider [tex]I_{1}[/tex] as the only source, and set [tex]I_{2} = 0 A[/tex]. The voltage across the circuit can be found using Ohm's law (V = IR), where R is the resistance in the circuit.

[tex]V_{1} = i1 * R = 6 A * 8 ohms = 48 V[/tex]

Next, consider [tex]I_{2}[/tex] as the only source, and set [tex]I_{1} = 0 A[/tex]. The voltage across the circuit can be found using Ohm's law (V = IR), where R is the resistance in the circuit.

[tex]V_{2} = i2 * R = 4 A * 8 ohms = 32 V[/tex]

Finally, the voltage across the circuit ([tex]V_{0}[/tex]) is the sum of the voltages found in steps 1 and 2.

[tex]V_{0} = V_{1} + V_{2} = 48 V + 32 V = 80 V[/tex]

So, the voltage across the circuit ([tex]V_{0}[/tex]) is 80 volts.

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Answer:

Step-by-step explanation:

ok so it is 100 amount budgeted i calculated all of them dont be mad if i did it wrong i am really bad at math and here is a calmng photo to calm you and elp you think

[tex]\sqrt{x}[/tex]