Please help with this math question!

Please Help With This Math Question!

Answers

Answer 1

The solution is, the expression is -3+0i, so, a = -3 & b = 0.

What is complex number?

In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted i, called the imaginary unit and satisfying the equation {\displaystyle i^{2}=-1}; every complex number can be expressed in the form a + bi, where a and b are real numbers.

here, we have,

So we have:

given that,

(2+6i) - (5+6i)

First, distribute:

2+6i - 5 -6i

Combine like terms:

2 - 5 + 6i - 6i

Add:

-3 + 0

So, in the a+bi format, we will have:

-3 + 0i

Hence, The solution is, the expression is -3+0i, so, a = -3 & b = 0.

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Related Questions

Find the accumulated value of an investment of

Answers

Part a: Compounded Semiannually: A = 20,771.75.

Part b: Compounded quarterly: A = 20817.66.

Part c: Compounded monthly: A = 20848.76

Part d: Compounded continuously :A = 407,538.49

Explain about compound interest?As the interest you earn on your savings starts to earn interest on itself, it is what is known as compound interest. As interest increases, it starts to accumulate more quickly and grows exponentially.

Compound interest formula:

A = P[tex](1 + \frac{r}{n} )^{nt}[/tex]

And

A = P[tex]e^{rt}[/tex]

Principal P : $15,000

Time t = 6 years

Rate of interest r = 5.5%

number of time compounded - n

Part a: Compounded Semiannually:

r --> r/2

n = 2

A = 15,000[tex](1 + \frac{0.055}{2} )^{2*6}[/tex]

A = 20,771.75

Part b: Compounded quarterly:

r --> r/4

n = 4

A = 15,000[tex](1 + \frac{0.055}{4} )^{4*6}[/tex]

A = 20817.66

Part c: Compounded monthly:

r --> r/12

n = 12

A = 15,000[tex](1 + \frac{0.055}{12} )^{12*6}[/tex]

A = 20848.76

Part d: Compounded continuously

A = Pe∧(rt)

A = 15,000(2.72)∧(0.55*6)

A = 407,538.49

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If we invest $40,000 at 8% simple interest, how much will we have saved in 20 years?

Answers

Answer:

$104,000

Step-by-step explanation:

For simple interest,

I = Prt

where I = interest earned

P = principal, amount invested

r = annual interest rate

t = time in years

I = $40,000 × 0.08 × 20

I = $64,000

The total amount saved is the principal amount plus the interest.

$40,000 + $64,000 = $104,000

why the nature of the roots depend on the value of the discriminant​

Answers

The value of a discriminant determines the kind of roots in a quadratic equation, and the sign of a discriminant indicates whether the roots were real or complex, unique or recurring.

What does a math quadratic equation mean?

Definitions: x ax2 + bx + c = 0 is a quadratic equation, which is a 2nd quadratic formula in a single variable. a 0. It has at most one solution since it is a 2nd quadratic problem, which is guaranteed by the algebraic basic theorem. The solution could be straightforward or difficult.

How do you determine whether an equation is quadratic?

To put it another way, if a twice the square of a expression that comes after b plus b times the same expression never squared plus c equals 0.

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Pls help i don’t know how to do this

Answers

Using the altitude or leg rule, we have:

x ≈ 42.7  

y = 40

z ≈ 53.4

How to Apply the Altitude or Leg Rule?

The leg rule is given as:

hypotenuse/leg = leg/part.

The altitude rule is:

left/altitude = altitude/right

To find the value of x, apply the altitude rule:

left = x

right = 24

altitude = 32

Substitute:

x/32 = 32/24

Cross multiply:

24x = 32²

24x = 1,024

x ≈ 42.7  

To find y, apply the leg rule:

leg = y

part = 24

hypotenuse = x + 24 = 42.7 + 24 = 66.7

Substitute:

66.7/y = y/24

y² = 1,600.8

y = √1x00.8

y = 40

To find z, apply the leg rule:

leg = z

part = x = 42.7  

Hypotenuse = 66.7

Substitute:

66.7/z = z/42.7

z² = 2,848.09

z = √2,848.09

z ≈ 53.4

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Find the H.C.F by division method a) 30,45,60​

Answers

The H.C.F. of 30, 45, and 60 using the division method is 30.

What is the HCF of the numbers?

To find the H.C.F. (Highest Common Factor) of the given numbers using division method, we can follow these steps:

Step 1: Divide the larger number by the smaller number and find the remainder.Step 2: Now, divide the smaller number obtained in the previous step by the remainder.Step 3: Continue this process of dividing the previous divisor by the remainder until the remainder becomes zero.Step 4: The last divisor obtained in the above process is the H.C.F. of the given numbers.

Let's apply this method to find the H.C.F. of 30, 45, and 60.

Step 1: We start by dividing the larger number, 60, by the smaller number, 30.

60 ÷ 30 = 2 with a remainder of 0

Step 2: Now, we divide the smaller number, 30, by the remainder, which is 0.

30 ÷ 0 = undefined

Since the remainder is zero, we stop the process here. The last divisor we obtained is 30. Therefore, the H.C.F. of 30, 45, and 60 is 30.

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1. Is A'B'C'D' a translation, rotation, or reflection of ABCD? Explain how you can tell. (2 points)
2. Is A"B"C"D" a translation, rotation, or reflection of A'B'C'D'? Explain. (2 points)
3. Suppose the measure of ∠B is 89°. Which other angles must measure 89°? How do you know? (3 points)
4. What is the perimeter of A"B"C"D"? Explain how you found the perimeter. (3 points)

Answers

Answer:

Step-by-step explanation: OK so is A'B'C'D' a translation, rotation, or reflection of ABCD? OK so A'B'C'D' is a rotation i believe because like you i'm on the same thing. Is A"B"C"D" a translation, rotation, or reflection of A'B'C'D'? OK so A"B"C"D" is a reflection i believe i'm not really sure on that one. Suppose the measure of angle B is 89°. Which other angle must be 89°? OK so angle A, angle C, and angle B. But I really don't get what you trying to ask? Hope I kind of helped, like i said im in 8th grade and it is kind of hard for me too.

the dot plot shows the number of wins for 16 baseball teams which statement about the data is true

Answers

Based on the dot plot, it appears that the data is spread relatively evenly across the teams, with no one team dominating the others by a wide margin.

What is data in math?

Data is the raw information that can be collected and analyzed to provide insights. It is the foundation of decision-making and can be used to identify trends, patterns, and relationships. Data can come from many different sources, including surveys, databases, and software applications. Data can be qualitative or quantitative, static or dynamic, structured or unstructured, and can be used to inform decisions, inform policy, and inform research. Data can also be used to make predictions, monitor performance, and improve efficiency.
This suggests that the competition between the teams is relatively balanced, and that no team is significantly outperforming the others in terms of number of wins. This could indicate that the teams are of about equal skill level, or that the schedule for each team is balanced enough that no team has an advantage over the others.

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You choose to invest $600 a year in a 401k which invests in an international stock mutual fund. Assuming an annual rate of turn of 9 percent, how much will this fund worth if retiring in 40 years?

Answers

The fund will be worth approximately $695,040 after 40 years if you invest $600 annually at a rate of 9 percent.
Final answer:

By using the future value of a series formula, you can calculate the future value of your investment. In this case, if you invest $600 annually in a 401k mutual fund with a 9% annual return, you will have approximately $132,204.02 after 40 years.

Explanation:

To solve this problem, we can use the future value of a series formula (also known as an annuity), which is common in business finance. The formula is:

FV = P * [((1 + r)^n - 1) / r]

Where:
FV is the future value of the money you have invested.
P is the annual investment (in this case, $600).
r is the annual rate of return (which is 9% or 0.09 as a decimal).
n is the number of years the money is invested (which is 40 in this scenario).

Applying these numbers to the formula we get:

FV = 600 * [((1 + 0.09)^40 - 1) / 0.09]

After performing the calculations, the future value (which is the amount of money you'll have at the end of 40 years) comes out to be approximately $132,204.02. Thus, if you invest $600 annually in a 401k which invests in an international stock mutual fund with a 9% annual rate of return, you will have $132,204.02 in the fund when retiring in 40 years.

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Review the graph of function g(x). On a coordinate plane, a curve starts at closed circle (4, negative 4), curves up to (3, negative 3), and curves down to (negative 1, negative 8), and then curves up through (negative 3, 4). A curve starts at open circle (4, 2) and curves up through (8, 5). What are Limit of g (x) as x approaches 4 negative and Limit of g (x) as x approaches 4 plus, if they exist? Limit of g (x) = 2 as x approaches 4 negative and limit of g (x) = negative 4 as x approaches 4 plus Limit of g (x) = negative 4 as x approaches 4 negative and limit of g (x) = negative 2 as x approaches 4 plus Limit of g (x) = negative 4 as x approaches 4 negative and limit of g (x) D N E as x approaches 4 plus Limit of g (x) D N E as x approaches 4 negative and limit of g (x) = negative 4 as x approaches 4 plus

Answers

The lateral limits of the function g(x) at x = 4 are given as follows:

[tex]\lim_{x \rightarrow 4^-} g(x) = -4, \lim_{x \rightarrow 4^+} g(x) = 2[/tex]

How to calculate the lateral limits?

To obtain lateral limits, we need to take the limit of a function as it approaches a point from the left-hand side and the right-hand side separately.

If the two limits are equal, then this is the limit of the function, while if the lateral limits are different, then the limit of the function does not exist for the value of x.

On a coordinate plane, a curve starts at closed circle (4, negative 4), curves up to (3, negative 3), and curves down to (negative 1, negative 8), and then curves up through (negative 3, 4), hence the lateral limit to the left of x = 4, where x is less than 4, is given as follows:

[tex]\lim_{x \rightarrow 4^-} g(x) = -4[/tex]

A curve starts at open circle (4, 2) and curves up through (8, 5), hence the lateral limit to the right of x = 4, where x is greater than 4, is given as follows:

[tex]\lim_{x \rightarrow 4^+} g(x) = 2[/tex]

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10. Jordan went to Europe for vacation. He spent of his time in Spain.
If he was in Spain for 14 days, how long was he in Europe?
Let v represent the number of days he was in Europe.
A v = 14
3
B (14) = v
C v ÷ 14 = ²

Answers

The number of days that he was in Europe will be 42 days.

How to calculate the days spent in Spain

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.

Since Jordan went to Europe for vacation. He spent 1/3 of his time in Spain.

If he was in Spain for 14 days, the number of days that he was in Europe will be:

1/3 × x = 14

x = (14 × 3)

x = 42 days

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Jordan went to Europe for vacation. He spent 1/3 of his time in Spain. If he was in Spain for 14 days, how long was he in Europe?

Please help!! See image bellow!!!

Answers

Answer:

consonance

Step-by-step explanation:

consonance are words that end the same

spins and veins

Bob ran 4/5 of a mile his sister ran one-half of a mile how much further did Bob run than his sister

Answers

30% or 3/10

Bob is 4/5

His sister is 1/2

convert to percents so 80% and 50%

he ran 30% more of a mile (3/10)

How many times 9 goes into 22

Answers

Answer: 22/9= 2.44444444 simplified 2.4
9 goes into 22 2.44 times.

Explanation:
22 divided 9 equals 2.44

4.3 GRE scores, Part I. Sophia who took the Graduate Record Examination (GRE) scored 160 on the Verbal Reasoning section and 157 on the Quantitative Reasoning section. The mean score for Verbal Reasoning section for all test takers was 151 with a standard deviation of 7, and the mean score for the Quantitative Reasoning was 153 with a standard deviation of 7.67. Suppose that both distributions are nearly normal.
(a) Write down the short-hand for these two normal distributions.
(b) What is Sophia’s Z-score on the Verbal Reasoning section? On the Quantitative Reasoning section? Draw a standard normal distribution curve and mark these two Z-scores.
(c) What do these Z-scores tell you?
(d) Relative to others, which section did she do better on?
(e) Find her percentile scores for the two exams.
(f) What percent of the test takers did better than her on the Verbal Reasoning section? On the Quantitative Reasoning section?

Answers

The normal distribution is N(151, 7), the z-score for verbal and quantitative reasoning are 1.29 and 0.52 respectively.

What is the short-hand for these two normal distribution

(a) The shorthand for the normal distribution of the Verbal Reasoning section is N(151, 7), where 151 is the mean score and 7 is the standard deviation. The shorthand for the normal distribution of the Quantitative Reasoning section is N(153, 7.67), where 153 is the mean score and 7.67 is the standard deviation.

(b) Sophia’s Z-score on the Verbal Reasoning section is (160-151)/7 = 1.29. Her Z-score on the Quantitative Reasoning section is (157-153)/7.67 = 0.52.

(c) The Z-scores represent how many standard deviations above or below the mean Sophia’s scores are. A Z-score of 1.29 on the Verbal Reasoning section means Sophia’s score is 1.29 standard deviations above the mean score of all test takers. A Z-score of 0.52 on the Quantitative Reasoning section means Sophia’s score is 0.52 standard deviations above the mean score of all test takers.

(d) Sophia did better on the Verbal Reasoning section because her Z-score is higher for that section.

(e) To find the percentile scores, we use the standard normal distribution table. Sophia’s percentile score on the Verbal Reasoning section is the percentage of test takers who scored lower than her. Using the Z-score of 1.29 and the table, we find that her percentile score is approximately 90.7%. Her percentile score on the Quantitative Reasoning section is the percentage of test takers who scored lower than her. Using the Z-score of 0.52 and the table, we find that her percentile score is approximately 69.4%.

(f) To find the percentage of test takers who did better than Sophia on each section, we can use the standard normal distribution table again. For the Verbal Reasoning section, we need to find the area to the right of Sophia’s Z-score of 1.29. Using the table, we find that this area is approximately 9.3%. Therefore, approximately 9.3% of test takers did better than Sophia on the Verbal Reasoning section. For the Quantitative Reasoning section, we need to find the area to the right of Sophia’s Z-score of 0.52. Using the table, we find that this area is approximately 30.4%. Therefore, approximately 30.4% of test takers did better than Sophia on the Quantitative Reasoning section.

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Suppose the same amount of snow fell the following​ winter, but the same amount of snow fell each week. How much snow fell each week if there were the same number of​ weeks?

​(Type a whole​ number, fraction, or mixed​ number.)

Answers

The amount of snow that fell each week was 2 units (assuming the units are consistent with the original scenario.

Describe Snowfall measurement?

Snowfall measurement is the process of determining the amount of snow that falls at a particular location during a specific period of time. Accurate snowfall measurement is important for a variety of reasons, including transportation safety, weather forecasting, and water resource management.

If the same amount of snow fell the following winter, but the same amount of snow fell each week, and there were the same number of weeks, then we need to divide the total amount of snow by the number of weeks to find the amount of snow that fell each week.

Looking at the diagram, we can estimate the total amount of snow that fell by counting the number of asterisks (*) in the diagram. There are 8 asterisks, which represent the total amount of snow that fell over the winter.

Since there are 4 weeks (the same number of weeks as the original scenario), we can divide the total amount of snow by 4 to find the amount of snow that fell each week:

Total amount of snow = 8 asterisks

Amount of snow that fell each week = Total amount of snow / Number of weeks

= 8 / 4

= 2

Therefore, the amount of snow that fell each week was 2 units (assuming the units are consistent with the original scenario).

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each year the population of algeland increases by 33% the population is currently 5,476,223. What will the population be 16 years from now

Answers

The required population of Algeland 16 years from now will be approximately 524937236.

What is Percentage?

In essence, percentages are fractions with a 100 as the remainder. We place the percent sign (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on an examination (75/100).

According to question:

To find the population of Algeland after 16 years, we can use the formula:

[tex]$P = P_0 \times (1 + r)^n$[/tex]

where P is the population after 16 years, [tex]$P_0$[/tex]is the initial population, r is the annual growth rate, and n is the number of years.

Given that the population of Algeland increases by 33% each year, we can express the annual growth rater as:

[tex]$r = 33% = 0.33$[/tex]% = 0.33

We are also given that the current population [tex]$P_0$[/tex] is 5,476,223.

Thus, the population of Algeland after 16 years can be calculated as:

[tex]$P = 5,476,223 \times (1 + 0.33)^{16}$[/tex]

Simplifying this expression, we get:

P = 524937236

Therefore, the population of Algeland 16 years from now will be approximately 524937236.

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The length of a rectangular poster is 8 more inches than two times its width. The area of the poster is 42 square inches. Solve for the dimensions (length and width) of the poster.

Answers

The dimensions of the poster are approximately 10.64 inches by 1.15 inches.

What are dimensions of an objects?

Dimension is the length or width of an area, region, or space in one direction. It is just the measurement of an object's length, breadth, and height.

According to the problem, the length of the poster is 8 more inches than two times the width, which can be expressed as:

length = 2x + 8

The area of the poster is given as 42 square inches, so we can set up the equation:

area = length * width

Substituting the expressions for length and width, we get:

42 = (2x + 8) * x

Expanding the right side, we get:

[tex]42 = 2x^2 + 8x[/tex]

Moving all terms to one side, we get:

[tex]2x^2 + 8x - 42 = 0[/tex]

Dividing both sides by 2, we get:

[tex]x^2 + 4x - 21 = 0[/tex]

We can solve for x using the quadratic formula:

x = (-4 ± √(4² - 41(-21))) / (2*1)

x = (-4 ± √88) / 2

x = (-4 ± 2√22) / 2

x = -2 ± √22

Since the width of the poster cannot be negative, we take the positive solution:

x = -2 + √22

Using this value, we can find the length of the poster:

length = 2x + 8 = 2(-2 + √22) + 8 = 2√22 + 4

Therefore, the length of the poster is approximately 10.64 inches (rounded to two decimal places).

Thus, the dimensions of the poster are approximately 10.64 inches by 1.15 inches.

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Write the equation of a rational function that has been translated left 2 units and shifted up 1 unit.​

Answers

The equation of a rational function that has been translated left 2 units and shifted up 1 unit is: f(x) = (a(x - 2) + b + 1) / (c(x - 2) + d)

What is a function?

A relation is a function if it has only One y-value for each x-value.

A general form of a rational function is:

f(x) = (ax + b) / (cx + d)

To translate this function left 2 units, we need to replace x with x + 2. This gives us:

f(x + 2) = (a(x + 2) + b) / (c(x + 2) + d)

To shift this function up 1 unit, we need to add 1 to the numerator. This gives us:

f(x + 2) = (a(x + 2) + b + 1) / (c(x + 2) + d)

Therefore, the equation of a rational function that has been translated left 2 units and shifted up 1 unit is: f(x) = (a(x - 2) + b + 1) / (c(x - 2) + d)

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The average American worker makes about 4x10^4 dollars yearly. The average professional basketball player makes about 6x10^6 dollars yearly. How many times greater is the average professional basketball player's salary than the average American worker's salary? {(WILL GIVE BRAINLIEST)}

Answers

Answer:150 times

Step-by-step explanation:

The average professional basketball player's salary is 6x10^6 dollars yearly, while the average American worker's salary is 4x10^4 dollars yearly.

To find how many times greater the average professional basketball player's salary is, we can divide the basketball player's salary by the worker's salary:

6x10^6 / 4x10^4 = (6/4)x10^(6-4) = 1.5x10^2 = 150

Therefore, the average professional basketball player's salary is 150 times greater than the average American worker's salary.

charlie has x pieces of candy .He shares ten with betsy and is left with 24 pieces of candy.Wich of the fowlling equations best reresents the situation

A)10+x=24
B)x+24=10
C)x-10=24

Answers

Answer:

2. x-10=24

Step-by-step explanation:

x is the unknown amount of candy that Charlie has.

He gives ten away (-10).

Now he has 24 pieces.

x-10 = 24

In a survey of consumers aged 12 and​ older, respondents were asked how many cell phones were in use by the household.​ (No two respondents were from the same​ household.) Among the​ respondents, 214 answered​ "none," 280 said​ "one," 373 said​ "two," 153 said​ "three," and 53 responded with four or more. A survey respondent is selected at random. Find the probability that​ his/her household has four or more cell phones in use. Is it unlikely for a household to have four or more cell phones in​ use? Consider an event to be unlikely if its probability is less than or equal to 0.05.
Question content area bottom
Part 1
​P(four or more cell ​phones)= enter your response here
​(Round to three decimal places as​ needed.)

Answers

Based on the information, it can be inferred that the probability that a person has four or more cell phones in their home is 0.0494

How to find the probability that a person has four or more cell phones in their home?

To find the probability that a person has four or more cell phones in their home, we must carry out the following mathematical procedure.

We must find the total number of people surveyed and the percentage that each group represents:

214 + 280 + 373 + 153 + 53 = 1,073

1,073 = 100%214 = ?214 * 100% / 1,073 = 19.94%

1,073 = 100%280 = %?280 * 100 / 1,073 = 26.09%

1,073 = 100%373 = %?373 * 100 / 1,073 = 34.76%

1,073 = 100%153 = %?153 * 100 / 1,073 = 14.25%

1,073 = 100%53 = %?53 * 100 / 1,073 = 4.93%

Now we must establish the probability. For this we must carry out the following mathematical procedure:

100% = 14.94% = ?4.94 * 1 / 100 = 0.0494

According to the above, the probability that someone answers that four or more cell phones are used in her house is 0.0494.

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Make P The Subject Of This Formula:: N= P-2t/15

Answers

Answer: P = 15N - 2t

Step-by-step explanation:

To find "P", we get rid of the last thing done to the subject (P).

Here it is "/15"

So we get rid of it by doing the opposite, remember, we do this to both sides.

Step 1:

             N = P - 2t/ 15

      x15 ↓                 ↓ ×15

              15N = P - 2t

Step 2:

Now, the last thing done to the "P" is "-2t". So we get rid of it by adding 2t to both sides.

                 15N = P - 2t

             +2t ↓             ↓ +2t

                  15N + 2t = P

So, we got P by its own, so we have made P the subject of the formula!

In summary, you would write the steps like this, to answer the question:
 

              N = P - 2t/ 15

      x15 ↓                 ↓ ×15

               15N = P - 2t  

           +2t ↓            ↓ +2t

               15N + 2t = P

               P = 15N - 2t

Make my answer the brainliest!

The fencing of the left border costs $8 per foot, while the fencing of the lower border costs $2 per foot. (No fencing is required along the river.) You want to spend $320 and enclose as much area as possible. What are the dimensions of your garden, and what area does it enclose?

Answers

The dimensions of the garden are 20 feet by 80 feet, and the area enclosed is 1600 square feet.

How is optimization employed in mathematics?

The process of selecting the optimal answer from a range of alternatives is known as optimization. In mathematics, optimization is employed to determine a function's maximum or least value. Typically, an optimization issue entails the optimization of a function under a set of restrictions.

Let's assume that the length of the left border is x feet.

The length of the lower border is y feet.

From the given situation the equation is:

8x + 2y = 320

To maximize the area of the garden, we maximize the product xy.

2y = 320 - 8x

y = 160 - 4x

Substituting this expression for y into the expression for the area, we get:

A = xy = x(160 - 4x) = 160x - 4x²

To find the value of x that maximizes the area, we can take the derivative of A with respect to x and set it equal to zero:

dA/dx = 160 - 8x = 0

x = 20

Substituting x = 20 back into the expression for y, we get:

y = 160 - 4x = 80

Therefore, the dimensions of the garden are 20 feet by 80 feet, and the area enclosed is: A = xy = (20)(80) = 1600 feet².

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algebra l
Find an exponential model that is a reasonable fit for the data.
The exponential model that is a reasonable fit for the data is ​f(x)=

Answers

The optimal strategy would be to fit several models to the data using equation mathematical software or tools, and then assess the goodness of fit using statistical metrics like R-squared or Mean Squared Error.

What is equation?

In a mathematical equation, the equals sign (=), which connects two claims and denotes equality, is utilised. In algebra, an equation is a mathematical statement that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a space. Mathematical expressions can be used to describe the relationship between the two sentences on either side of a letter. The logo and the particular piece of software frequently correspond. like, for instance, 2x - 4 = 2.

The following exponential model could be a good fit for the data in the image:

[tex]f(x) = 7.5 * e^(0.1x) (0.1x)[/tex]

The data is assumed to develop exponentially with a base of e in this model, with a growth rate of 10% for each unit increase in x.

It is crucial to remember that this is only one potential model and that other exponential models with other parameters could also be able to satisfactorily match the data. The optimal strategy would be to fit several models to the data using mathematical software or tools, and then assess the goodness of fit using statistical metrics like R-squared or Mean Squared Error.

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For Saturday matinees, a movie theater charges $5 for adult tickets and $3 for children's tickets. If the movie theater sold a total of 166 matinee tickets and made
$718 in revenue on Saturday afternoon, how many adult matinee tickets were sold?

Answers

Answer:

Let's use A to represent the number of adult tickets sold and C to represent the number of children's tickets sold.

We know that A + C = 166, since the total number of tickets sold is 166.

We also know that the revenue earned from adult tickets is $5A and the revenue earned from children's tickets is $3C. Since the total revenue earned is $718, we can write:

5A + 3C = 718

Now we have two equations with two variables:

A + C = 166

5A + 3C = 718

We can solve for A in the first equation to get:

A = 166 - C

Then we can substitute this expression for A into the second equation:

5(166 - C) + 3C = 718

Simplifying and solving for C, we get:

830 - 2C = 718

2C = 112

C = 56

So 56 children's tickets were sold. We can substitute this value back into the first equation to solve for A:

A + 56 = 166

A = 110

Therefore, 110 adult tickets were sold.

Answer:

Step-by-step explanation:

Let's use the following variables:

a = number of adult tickets sold

c = number of children tickets sold

We know that:

a + c = 166 (total number of tickets sold)

5a + 3c = 718 (total revenue)

We can solve this system of equations by substitution or elimination. Here, we'll use elimination:

Multiply the first equation by 3: 3a + 3c = 498

Subtract the second equation from the first: 2a = 220

Solve for a: a = 110

So 110 adult tickets were sold. We can find the number of children's tickets by substituting a = 110 into either of the original equations:

c = 166 - a = 166 - 110 = 56

Therefore, 110 adult tickets and 56 children's tickets were sold.

Determine whether the study is an experiment or an observational​ study, and then identify a major problem with the study.
In a​ survey, 1465 Internet users chose to respond to this question posted on a​ newspaper's electronic​ edition: "Is news online as satisfying as print and TV​ news?" 52% of the respondents said​ "yes."
Question content area bottom
Part 1
This is an

experiment
observational study
because the researchers

do not attempt to modify
apply a treatment to
the individuals.
Part 2
What is a major problem with the​ study?
A.
This is a convenience sample with voluntary​ response, which has a high chance of leading to bias.
B.
There is no blinding or​ replication, which has a high chance of leading to bias.
C.
The sample is not very large.
D.
The results apply only to Internet users

Answers

The study is classified as an observational study, and the problem is given as follows:

A.

This is a convenience sample with voluntary​ response, which has a high chance of leading to bias.

What are experiments and observational studies?

Experiments are studies in which there are two groups, with different features, and then the effect of a feature is studied.

For an observational study, there are no changes, just a question is asked, as is the case for this problem.

Convenience samples lead to bias as many people that share characteristics can answer.

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Create a Venn diagram to illustrate the following:
(D ⋃ E) ⋃ F

Answers

The Venn diagram for (D ⋃ E) ⋃ F will be the ovarlapped region of D,E and F.

What exactly is a Venn diagram?

A Venn diagram is a graphical representation of set theory that uses circles or other closed shapes to show the relationships between sets of objects. In a Venn diagram, each set is represented by a circle or other shape, and the area of the circle represents the total number of objects in that set.

The circles are usually drawn so that they overlap, with the overlapping region representing the objects that belong to both sets. Venn diagrams can be used to illustrate set operations such as union, intersection, and complement.

Now,

As i can not draw here

so i will explain it

To create the Venn diagram, we first draw three overlapping circles to represent the sets D, E, and F. We then shade the regions corresponding to the set operations in the expression, starting from the innermost operation and working our way out.

The expression (D ⋃ E) represents the union of sets D and E, so we shade the region where the circles for D and E overlap. This region represents all the elements that are in D or E or both.

Next, we take the union of (D ⋃ E) with F. This means we shade the region where the circle for F overlaps with the region we shaded in the previous step. This region represents all the elements that are in D or E or F or any combination of these sets.

The final Venn diagram should have three overlapping circles, with the region where all three circles overlap shaded to represent (D ⋃ E) ⋃ F.

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Atul gets a pocket money allowance of Rs.120 per day. Thinking that this was rather less he asked his friends about their allowances and obtained the following data which includes his allowance also ( Amount I Rs.) 120, 180, 100, 50, 250, 200,200,220, 150, 100,100,150,130,200,180, 100, 150, 100, 180, 150, 120, 150, 100, 150, 100, 120, 180, 200, 50.
He presented this data to his father and asked for an increase in his allowance as he was getting less than average amount. His father, a statistician, countered pointing out that Atul's allowance was actually more than the average amount.

Answers

Atul's father is mistaken, and Atul's request for an increase in his allowance may be valid based on the information given.

What is Statistics?

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

To determine whether Atul's allowance is above or below the average, we need to calculate the average allowance for all the friends, including Atul.

To do his, we add up all the amounts and divide by the total number of friends:

Average allowance = (120+180+100+50+250+200+200+220+150+100+100+150+130+200+180+100+150+100+180+150+120+150+100+150+100+120+180+200+50) / 29

Average allowance = 162.07

So, the average allowance for Atul's friends, including himself, is Rs. 162.07 per day.

Since Atul's allowance is Rs. 120 per day, we can see that his allowance is actually less than the average.

Therefore, Atul's father is mistaken, and Atul's request for an increase in his allowance may be valid based on the information given.

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Necesito estas respuestas

Answers

The scale factor for the given transformation is -

{k} = 2/3.

What is scale factor in mathematics?

A scale factor in math is the ratio between corresponding measurements of an object and a representation of that object.

Given is a figure {Q} that is a transformation of figure {P}.

The base length of the figure {P} is 15 cm. The base length for figure {Q} is 10 cm. So, we can write the scale factor as -

{K} = 10/15

{K} = 2/3

Therefore, the scale factor for the given transformation is -

{k} = 2/3.

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Evaluate the expression 4xy-(x+7) if x=-2 and y=5

Answers

Given:-

[tex] \tt \: x = -2[/tex]

[tex] \: [/tex]

[tex] \tt \: y = 5[/tex]

[tex] \: [/tex]

Solution:-

[tex] \tt \: 4xy - ( x + 7 )[/tex]

now , put the given values of x = -2 nd y = 5 in equation :

[tex] \: [/tex]

[tex] \tt \: 4( -2 ) ( 5 ) - ( -2 + 7 )[/tex]

[tex] \: [/tex]

[tex] \tt \: -8( 5 ) - 5[/tex]

[tex] \: [/tex]

[tex] \tt \: -40 - 5[/tex]

[tex] \: [/tex]

[tex] \boxed{ \tt{ \orange{ \:-45 \: }}}[/tex]

[tex] \: [/tex]

━━━━━━━━━━━━━━━━━━━━━━━━━━━

hope it helps! :)

Answer:-45

Step-by-step explanation:

first plug in the x and the y values

4(-2)(5)-(-2+7)

The start using pemdas to simplify

*or bodmas depends on what you learned

Then you should arrive to this

4(-2)(5)+ -(5)

-8(5)+ -5

-40-5= -45

Hope that helps

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