a wise man once said, “ 400 reduced by 3 times my age is 163”. what is his age?

Answer:

Additive inverses for complex numbers are just like they are for real numbers: they mean the number you'd add to get back to 0. Just like real numbers, this means that you change the signs. Thus, the additive inverse of -4+7i is 4-7i

hope it helps

Step-by-step explanation:

Answer:

x = 9

Step-by-step explanation:

if the perimeter os square JKLM is 48  

each side has 48/4

so each side has 12

now if JK is x + 3 = 12

we only need to solve that

x + 3 = 12

x = 12 -3

x = 9

Answer:

B. 9

Step-by-step explanation:

Answer:

846,45cm³

Step-by-step explanation:

V = 9.5 * 6 * 16.5

V = 940.5cm³

90% = 940.5 * 0.9 = 846,45cm³

Answer:

0.85 liters

Step-by-step explanation:

Step 1. Find the volume of the full prism

V=9.5 x 6 × 16.5 = 940.5 [tex]cm^{3}[/tex]

Step 2. Find 90% of the full volume of the prism

90% x 940.5 = 0.9 × 940.5 = 846.45 [tex]cm^{3}[/tex]

Step 3. Convert [tex]cm^{3}[/tex] to liters (1 liter = 1000 [tex]cm^{3}[/tex]    )

846.45 [tex]cm^{3\\[/tex] = 0.84645 ≈ 0.85

Answer - 0.85 liters

Answer:

The 24th Customer is the first to get two gift certificates.

Since, 2 x 2 x 2 x 2 x 3 = 24

The first customer to receive two gift certificates is the customer at the 24th position in the sequence of customers.

The LCM of 8 and 6 is 24. This means that the first customer to receive two gift certificates will be the one who appears at the 24th position in the sequence.

To calculate the position of this customer, we can consider the multiples of 24:

24, 48, 72, and so on.

The 24th customer is the first to receive two gift certificates, as they satisfy both the every-8th and every-6th customer criteria.

The Greatest Common Factor (GCF) and the Least Common Multiple (LCM) are fundamental concepts in number theory. The GCF of two or more numbers is the largest positive integer that divides all the given numbers without leaving a remainder. On the other hand, the LCM of two or more numbers is the smallest positive multiple that is divisible by all the given numbers.

In this scenario, the GCF and LCM were used to determine the customer who would receive two gift certificates. The GCF was not explicitly required to solve this particular problem, but it is a useful concept in various mathematical contexts.

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Complete Question:

To celebrate its grand opening, a store is giving -customers gift certificates. Which customer is the first to get two gift certificates? Every 8 th customer gets Every 6th customer gets a $10 gift certificate. 200 4-2 Find Greatest Common Factor and Least Common Multiple

Final answer:

To find the distance from X to line AC, we can use the angle bisector theorem and the fact that M is the midpoint of AB. By substituting the known values, we can solve for the distance d and find that X is 12 units away from line AC.

Explanation:

We are given that M is the midpoint of side AB of triangle ABC. Angle bisector AD of angle CAB and the perpendicular bisector of side AB meet at X. We are also given that AB = 40 and MX = 9.

To find the distance from X to line AC, we can use similar triangles. Let's denote the distance from X to line AC as d. According to the angle bisector theorem, we have:

AD/CD = AB/CB

Since M is the midpoint of AB, we have:

MD = MB = AB/2 = 40/2 = 20

Therefore, we can rewrite the angle bisector theorem as:

AD/(AD + CD) = AB/CB

Substituting the known values, we get:

9/(9 + d) = 40/20

Cross multiplying, we have:

20 * 9 = 40 * (9 + d)

Simplifying, we find:

d = 12

Therefore, X is 12 units away from line AC.

Answer:

Fractional form = [tex]\frac{95}{100}=\frac{19}{20}[/tex]

Percent form = 95%

Trisha got 95% of her problems correct.

Step-by-step explanation:

Given:

Total number of questions (N) = 100

Number of correct questions (C) = 95

Therefore, the ratio of the correct answers to the total number of problems is given by dividing the the number of correct questions by the total number of questions. This is given as:

Ratio expressed as a fraction = [tex]\frac{C}{N}=\frac{95}{100}=\frac{95\div 5}{100\div 5}=\frac{19}{20}(Simplest\ form)[/tex]

Now in order to express this ratio in percentage form, we need to multiply the given ratio by 100. This gives,

Ratio expressed as a percent = [tex]\frac{C}{N}\times 100=\frac{95}{100}\times 100=95\%[/tex]

Therefore, Trisha got 95% of her problems correct.

Answer:

1: the first one

2:the third one

3:the third one

Step-by-step explanation:

Answer:

a) 43 m b) 55 m

Step-by-step explanation:

a) From question at t = 0, initial velocity [tex]V_{o}[/tex] = 15 m/s

   Using equation of motion, [tex]S = V_{o}t + \frac{1}{2} at^{2}[/tex] ; at t = 2 secs , a = 4 m/[tex]s^{2}[/tex]

    S = (15 x 2) + (0.5 X 4 x [tex]2^{2}[/tex])

    S = 30 + 8 = 38 m , Therefroe;

  car is (38 + 5)m from the sign post

  car is 43 m from the sign post at t = 2 secs

b) Also from equation of motion, [tex]V^{2} = V_{o} ^{2} + 2aS[/tex]

    [tex]25^{2} = 15^{2}[/tex] + (2 x 4 x S)

     625 - 225 = 8S

S = 50 m

 Car is (50 + 5) m from the sign post

Car is 55 m from the sign post at V = 25 m/s

At t=2s, the motorcyclist is at position 29m east of the signpost with a velocity of 23m/s. When his velocity is 25m/s, he is at a position 38.75m east of the signpost.

Given that the motorcyclist starts 5 m east of the signpost with an initial velocity of 15 m/s and a constant acceleration of 4.0 m/s2, we can use the equation of motion to find his position and velocity at any given time.

(a) At t=2s, the motorcyclist's position (x) and velocity (v) can be determined using the following two equations respectively:

(b) When the velocity is 25 m/s, the time can be calculated using the equation v = v0 + a*t. By setting v=25m/s, v0=15m/s, and a=4.0m/s2, we get t = (25m/s-15m/s) / 4.0m/s2 = 2.5s. Substituting this time into the position equation gives x = 5m + 15m/s*2.5s + 0.5*4.0m/s2*(2.5s)2, which results in the motorcyclist being at position 38.75 m.

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Step-by-step explanation:

Hope it helps you in your learning process.

Answer:

Θ = 0, [tex]\frac{7\pi }{6}[/tex], [tex]\frac{11\pi }6}[/tex]

Step-by-step explanation:

sin(theta) + 1 = cos^2(theta) - sin^2(theta)

sin(theta) + 1 = (1 - sin^2(theta)) -sin^2(theta)

sin(theta) = -2sin^2(theta)

2sin^2(theta) + sin(theta) = 0

sin(theta)[2sin(theta) + 1] = 0

sin(theta) = 0 and 2sin(theta) + 1 = 0

sin(theta) = 0 and sin(theta) = -1/2

Θ = 0, [tex]\frac{7\pi }{6}[/tex], [tex]\frac{11\pi }6}[/tex]

Answer:

For the sequence is [tex]-\frac{2}{3}[/tex] ,-4 ,-24 ,-144 ,...

Hence the formula [tex]f(x)=-\frac{2}{3}(6)^{x-1}[/tex] for x=1,2,3,... represents the given geometric sequence

Step-by-step explanation:

Given sequence is [tex]-\frac{2}{3}[/tex] ,-4 ,-24 ,-144 ,...

To find the formula to describe the given sequence :

Let [tex]a_1=\frac{-2}{3}[/tex] ,[tex]a_2=-4[/tex] ,[tex]a_3=-24[/tex],...

First find the common ratio

[tex]r=\frac{a_2}{a_1}[/tex] here  [tex]a_1=\frac{-2}{3}[/tex] and,[tex]a_2=-4[/tex]

[tex]=\frac{-4}{\frac{-2}{3}}[/tex]

[tex]=\frac{4\times 3}{2}[/tex]

[tex]=\frac{12}{2}[/tex]

[tex]r=6[/tex]

[tex]r=\frac{a_3}{a_2}[/tex] here  [tex]a_2=-4[/tex] and [tex]a_3=-24[/tex]

[tex]=\frac{-24}{-4}[/tex]

[tex]=6[/tex]

[tex]r=6[/tex]

Therefore the common ratio is 6

Therefore the given sequence is geometric sequence

The nth term of the geometric sequence is

[tex]a_n=a_1r^{n-1}[/tex]

The formula which describes the given geometric sequence is

[tex]f(x)=a_1r^{x-1}[/tex] for x=1,2,3,...

[tex]=\frac{-2}{3}6^{x-1}[/tex] for x=1,2,3,...

Now verify that [tex]f(x)=a_1r^{x-1}[/tex] for x=1,2,3,... represents the given geometric sequence or not

put x=1 and the value of [tex]a_1[/tex] in [tex]f(x)=a_1r^{x-1}[/tex] for x=1,2,3,...

we get [tex]f(1)=-\frac{2}{3}(6)^{1-1}[/tex]

[tex]=-\frac{2}{3}(6)^0[/tex]

[tex]=-\frac{2}{3}[/tex]

Therefore [tex]f(1)=-\frac{2}{3}[/tex]

put x=2 we get [tex]f(2)=-\frac{2}{3}(6)^{2-1}[/tex]

[tex]=-\frac{2}{3}(6)^1[/tex]

[tex]=-\frac{12}{3}[/tex]

Therefore [tex]f(2)=-4[/tex]

put x=3 we get [tex]f(3)=-\frac{2}{3}(6)^{3-1}[/tex]

[tex]=-\frac{2}{3}(6)^2[/tex]

[tex]=-\frac{2(36)}{3}[/tex]

Therefore [tex]f(3)=-24[/tex]

Therefore the sequence is f(1),f(2),f(3),...

Therefore  the sequence is [tex]-\frac{2}{3}[/tex] ,-4 ,-24 ,-144 ,...

Hence the formula [tex]f(x)=a_1r^{x-1}[/tex] for x=1,2,3,... represents the given geometric sequence is verified

Therefore the formula [tex]f(x)=-\frac{2}{3}(6)^{x-1}[/tex] for x=1,2,3,... represents the given geometric sequence

Answer:

a

Step-by-step explanation:

Answer:

[tex]f(x)=100(\frac{3}{5} )^x[/tex]

Step-by-step explanation:

Since the exponential function approaches y=0, its equation is of the form,

[tex]f(x)=a(b^x)[/tex]

The point (0,100) is this graph so it must satisfy its equation

[tex]100=a*b^0[/tex]

[tex]100=a(1)[/tex]

a=100

The equation now becomes:

[tex]f(x)=100*b^x[/tex]

We now substitute the point (1,60)

[tex]60=100*b^1[/tex]

[tex]b=\frac{60}{100} =\frac{3}{5}[/tex]

Therefore the required equation is [tex]f(x)=100(\frac{3}{5} )^x[/tex]

Answer:

the correct answer is A

Step-by-step explanation:

Answer:

View graph

Step-by-step explanation:

we have that at constant speed the student and the pet must travel equal distances in equal times, so they must be in the middle of the distance with the same travel time

As can be seen in graph 2 the distance of P = -15 m, and that of S = 15, the sign is due to the orientation, P goes to the left and S to the right

Answer:

The data claims that 90% of the seeds are viable meaning that 90% of the seeds are likely to germinate and grow into healthy plants under good conditions.90% 0f 1000seeds gives 900seeds,and 903seeds germinated so the claim is true

Step-by-step explanation:

Total number of seeds=1000

Seeds that germinate =903

90% of 1000=>90/100×1000 =900seeds.

Answer: 6 feet x 3 feet

Step-by-step explanation:

Let the height be given by= x

The length is= 6x -2 (1) from both sides= 6x-2

The width is= 3x-2(1) from both sides= 3x-2

The total volume= length * width * height

4=(6x-2)*(3x-2)*x

Solving we get,

x=1 and other factor is not the valid option.

So the outer dimensions should be 6 feet x 3 feet

Answer:

The Final answer will be [tex]2x^2+5x+2[/tex] with remainder 0.

Step-by-step explanation:

We have attached the division for your reference.

Given:

Dividend = [tex]6x^3 + 11x^2 - 4x -4[/tex]

Divisor= [tex]3x - 2[/tex]

Explaining the division we get;

Step 1: First when we divide the Dividend [tex]6x^3 + 11x^2 - 4x -4[/tex] with divisor [tex]3x - 2[/tex] we will first multiply [tex]2x^2[/tex] with the divisor then we get the Quotient as [tex]2x^2[/tex] and Remainder as [tex]15x^2-4x-4[/tex]

Step 2: Now the Dividend is [tex]15x^2-4x-4[/tex] and Divisor is [tex]3x - 2[/tex] we will now multiply [tex]5x[/tex] with the divisor then we get the Quotient as [tex]2x^2+5x[/tex] and Remainder as [tex]6x-4[/tex]

Step 3: Now the Dividend is [tex]6x-4[/tex] and Divisor is [tex]3x - 2[/tex] we will now multiply 2 with the divisor then we get the Quotient as [tex]2x^2+5x+2[/tex] and Remainder as 0.

Hence The Final answer will be [tex]2x^2+5x+2[/tex] with remainder 0.

Answer:

3/2

Step-by-step explanation:

Answer:

3/2

Step-by-step explanation:

9 to 6 means  

                                                          [tex]\dfrac{9}{6}[/tex]

Now we will cancel that fraction - we will divide numerator and denominator both by 3:

9 divided by 3 equals 3

6 divided by 3 equals 2

Hence,

                                        [tex]\dfrac{9}{6} = \dfrac{3\cdot 3}{2\cdot 3} = \dfrac{3}{2}[/tex]

The area of circle is 2463.0086 cm².

Step-by-step explanation:

Given,

Diameter of circle = 56 cm

Radius of circle = [tex]\frac{Diameter}{2}[/tex]

Radius of circle = [tex]\frac{56}{2}=28\ cm[/tex]

We know that;

Area of circle = [tex]\pi r^2[/tex]

Area of circle = [tex]\pi *(28)^2[/tex]

Area of circle = π * 784

Area of circle = 2463.00864041 cm²

Rounding off to four decimal places

Area of circle = 2463.0086 cm²

The area of circle is 2463.0086 cm².

Keywords: area, circle

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Answer:

The answer is B) 3

Step-by-step explanation:

The reason why is because 1 is less than OR equal to x and 3 is less than or equal to x and is x = 3 then it fits both descriptions the best.

Answer:

-3

Step-by-step explanation:

3 is the average rate of change for the exponential graph shown over the interval 1 ≤ x ≤ 3.

Start by determining the two distinct points: (1, 2) and (3, −4).

Therefore,  

Δf(x)

Δx

=  

−4 − 2

3 − 1

=  

−6

2

= −3

Answer :

The required number is 2.

Step-by-step explanation:

Given : The sum of six fifths and six times a number is equal to four fifths subtracted from seven times the number.

To find : The number ?

Solution :

Let the number be 'x'.

The sum of six fifths and six times a number i.e.  [tex]\frac{6}{5}+6x[/tex]

Four fifths subtracted from seven times the number i.e. [tex]7x-\frac{4}{5}[/tex]

According to question,

[tex]\frac{6}{5}+6x=7x-\frac{4}{5}[/tex]

[tex]7x-6x=\frac{6}{5}+\frac{4}{5}[/tex]

[tex]x=\frac{10}{5}[/tex]

[tex]x=2[/tex]

The required number is 2.

Final answer:

In a time series, an explainable one-time variation is known as an outlier. Outliers can be important for understanding data, but they differ from inexplicable random components which include variations not explained by trend, cyclical, or seasonal patterns.

Explanation:

In the context of data patterns in a time series, a one-time variation that is explainable is usually referred to as an outlier. An outlier can be a potential key to understanding the data or it may be due to some abnormality or error. In a time series, data is analyzed over time to determine components such as the trend, cyclical, seasonal, and random components.

Trend component displays the long-term progression of the series, the cyclical component deals with fluctuations occurring at non-fixed intervals, the seasonal component reflects regular variations within a specific period, like quarters within a year, and the random component comprises those elements that cannot be attributed to the trend, cyclical, or seasonal patterns.

It's essential to distinguish outliers from the random components, which are, by definition, inexplicable variations. However, if an outlier can be explained by a particular event or change, it's not part of the random component but a distinct deviation from the expected pattern.

Answer:

Step-by-step explanation:

An arc is a portion of the circle's circumference bounded by 2 radii

The formula for determining the length of an arc is expressed as

Length of arc = θ/360 × 2πr

Where

θ represents the central angle or angle which the 2 radii subtends at the center of the circle.

r represents the radius of the circle.

π is a constant whose value is 3.14

From the information given,

Radius, r = 5 inches

θ = 170 degrees

Therefore,

Length of arc = 170/360 × 2 × π × 5

Length of arc = 4.7222π feet

rounding up to 2 decimal places, it becomes

4.72π feet

Answer:

It should be option B

Step-by-step explanation:

To find the number of students the North and South campuses had before the merger, set up an equation and solve for the unknowns. Use the given percentages and total number of students to determine the number of music majors at each campus.

To find the number of students the North and South campuses had before the merger, we can set up two equations based on the given information. Let's assume the number of students at the North campus is N and the number of students at the South campus is S.

From the information provided, we know that 30% of the students at the North campus are music majors, so the number of music majors at the North campus is 0.3N. Similarly, 80% of the students at the South campus are music majors, so the number of music majors at the South campus is 0.8S.

Since the campuses are merged into the East campus, which has 1000 students and 45% of them are music majors, we can set up the equation 0.45(1000) = 0.3N + 0.8S to represent the total number of music majors at the East campus. From this equation, we can solve for N and S to find the number of students at the North and South campuses before the merger.

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Answer:

So, with one measurement, we can determine the bag of gold coins.

Step-by-step explanation:

We will number the bags with numbers from 1 to 100. Then we will take one coin from the first bag, from the second we will take 2 coins, from the third we will take 3 coins. We will continue the process to the last bag, from which we will take all 100 coins. Then we'll put it all on a digital scale.

Depending on how many numbers in the decimal notation we mean what the bag of gold coins is. For example, if the decimal number is .02, we will conclude that 2 is a bag of gold coins. For example, if the decimal number is .33, we would conclude that 33 is a bag of gold coins. If there are no decimal numbers, we conclude that the gold bag is the last bag on the digital scale, because 100 · 1.01 = 101.

So, with one measurement, we can determine the bag of gold coins.

Final answer:

The block lava has flowed 45 meters from the base of the volcano after 30 days, based on a rate of 1.5 meters per day.

Explanation:

To calculate how far the block lava has flowed from the base of a volcano after 30 days at a rate of 1.5 meters per day, we simply multiply the rate of flow by the number of days.

Distance traveled = Rate × Time

Distance traveled = 1.5 meters/day × 30 days = 45 meters.

So, if the lava continues to flow at this constant rate, after 30 days, it will have moved 45 meters away from the base of the volcano. This calculation offers valuable insights into the potential extent of volcanic activity, aiding in risk assessment and mitigation strategies for areas surrounding the volcano.

Question: on saturday, a minor league baseball team gave away baseball cards to each person entering the stadium. One group received 28 baseball cards . a second group received 68 baseball cards. If each person entering the stadium received the same number of cards, what was the greatest possible number of cards that each person could have received?

Answer:

4 baseball cards

Step-by-step explanation:

Since each person entering the stadium receive the same number of cards, we look for the Highest Common Factors HCF of the number of members of the groups.

The factors of 28 = 1 x 2² x 7

The factors of 68 = 1 x 2² x 17

Looking at the factors, the higest common factor HCF is 2² or 4.

This implies that the higest possible number of baseball cards that each person would have received is 4 baseball cards

Answer: $4959.50

Step-by-step explanation:

We would apply the formula for determining compound interest which is expressed as

A = P(1+r/n)^nt

Where

A = total amount in the account at the end of t years

r represents the interest rate.

n represents the periodic interval at which it was compounded.

P represents the principal or initial amount deposited

From the information given,

P = 4400

r = 6% = 6/100 = 0.06

n = 12 because it was compounded 12 times in a year.

t = 2 years

Therefore,

A = 4400(1 + 0.06/12)^12 × 2

A = 4400(1+0.005)^24

A = 4400(1.005)^24

A = 4959.5

Answer:

b. 4.1 shirts

Step-by-step explanation:

Given data:

number of terms = 12

Terms given are 3, 4, 8, 5, 2, 5, 0, 5, 3, 4, 3, 7

Mean = (sum of terms)/ (number of terms)

Mean = (3 +4+ 8+ 5+2+5+0+ 5+ 3+ 4+3+ 7)/12

Mean = 49/12

Mean = 4.083

Mean = 4.1 (to the nearest tenth)

Answer:

Answer is 4.1 shirts.

Step-by-step explanation:

Answer:

Could be 6

Step-by-step explanation:

The reason I'm saying could is that I don't know of any mathematical system that uses the word twice. I could very easily be wrong. As far as I know twice means double, though.

Twice 3 most likely means like two times of 3,or 3 of something two times.or 3 times two..I hope thi helps in any way.

Answer:

See explanation

Step-by-step explanation:

Linear expression is usually an expression of 1st degree.

A. The product of a number and seven [tex]=7\cdot n=7n[/tex]

Correct, linear

B. The sum of three consecutive numbers.

Let the smallest number be n, the next number is n + 1 and the last number is n + 2. Then their sum is

[tex]n+(n+1)+(n+2)[/tex]

Correct, linear

C. ​The square of a number times three.

Let the number be n, then its square is [tex]n^2[/tex] and the square of a number times three is

[tex]n^2\cdot 3=3n^2[/tex]

Correct, nonlinear

D. ​Twice the sum of a number and 8.

If the number is n, then the sum of the number anf 8 is n + 8. Twice the sum is

[tex]2\cdot (n+8)=2(n+8)[/tex]

Incorrect, linear

E. The cube of a number divided by two.

If the number is n, then its cube is [tex]n^3.[/tex] The cube of the number divided by 3 is

[tex]n^3\div 3[/tex]

Correct, nonlinear

Answer:

Step-by-step explanation:

The perimeter of a plane figure is the distance around the figure.

Lyric's garden is triangular. The formula for determining the perimeter of a triangle is expressed as

Perimeter = a + b + c

Where a, b and c are the side lengths of the triangle.

Since the triangle is a right angle triangle, to determine the length, c of the third side, we would apply Pythagoras theorem. It is expressed as

Hypotenuse² = opposite side² + adjacent side²

c² = 10² + 7² = 100 + 49

c = √149 = 12.2 feet

The number of feet of fencing that Lyric needs to enclose the triangular garden is

10 + 7 + 12.2 = 29.2 feet

Final answer:

Lyric will need approximately 29.2 feet of fencing to enclose her garden, which is calculated using the Pythagorean theorem to find the hypotenuse of the right triangle and then adding all sides for the perimeter.

Explanation:

To determine how much fencing Lyric will need for her garden, we have to find the perimeter of the right triangle. We are given the base and the height, which are 10 feet and 7 feet respectively.

To find the length of the hypotenuse, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Calculating,

Hypotenuse = √(base2 + height2)
= √(102 + 72)
= √(100 + 49)
= √149
= 12.2 feet (rounded to the nearest tenth)

Now, to find the total amount of fencing required, we add the lengths of all three sides of the triangle:

Total fencing needed = base + height + hypotenuse
= 10 feet + 7 feet + 12.2 feet
= 29.2 feet (rounded to the nearest tenth)

Therefore, Lyric will need approximately 29.2 feet of fencing to enclose her garden.

x° = 43° and y° = 120°

Solution:

Given ABCD is a parallelogram.

∠A = (y + 9)°, ∠C = (3x)°, ∠D = (x + 8)°

In a parallelogram, sum of the adjacent angles = 180°

⇒ ∠C + ∠D = 180°

⇒ (x + 8)° + (3x)° = 180°

⇒ x° + 8° + 3x° = 180°

⇒ 4x° + 8° = 180°

⇒ 4x° = 180° – 8°

⇒ 4x° = 172°

⇒ x° = 43°

Substitute x° = 43° in ∠C.

∠C = (3x)°

     = 3 × 43°

∠C = 129°

In parallelogram, opposite angles are equal.

⇒ ∠A = ∠C

⇒ ∠A = 129°

⇒ (y + 9)° = 129°

⇒ y° = 129° – 9°

⇒ y° = 120°

Hence the value of x° = 43° and y° = 120°.

Answer:

120 degrees

Step-by-step explanation: