-4(-5+x)>56
??? whats the answer

Answers

Answer 1

Answer:

x < -9

Step-by-step explanation:

-4(-5+x)>56 (given)

20 - 4x >56 (distributive property of inequality)

-4x > 36 (subtraction property of inequality)

x < -9 (division property of inequality)

The sign flips since it was divided by a negative number.


Related Questions

Please help I’m being timed!!! A country commits to decreasing spending for infrastructure in various ways at a rate of 30% per year. At the time of the announcement, the country is spending $12 billion per year. Which graph models the amount of infrastructure spending for future years?

Please help Im being timed!!! A country commits to decreasing spending for infrastructure in various
Please help Im being timed!!! A country commits to decreasing spending for infrastructure in various
Please help Im being timed!!! A country commits to decreasing spending for infrastructure in various
Please help Im being timed!!! A country commits to decreasing spending for infrastructure in various

Answers

Answer:

It would be the graph that has point (0,12) and is decreasing to the right.

A man buys a car for rs.80000 and spends rs.20000 more for repairing. He sells it at rs.125000. Find his gain percent. ​

Answers

Answer:

25%

Step-by-step explanation:

Given:

The man buys the car for 80000 units.

For repairing the car, the man spends 20000 units.

The man sells the car for 125000 units.

To find:

The gain percent of the man.

Solution:

The man buys the car for 80000 units.

For repairing the car, the man spends 20000 units.

∴ Total expenditure of the man for the car_

(80000 + 20000) units.

= 100000 units.

The man sells the car for 125000 units.

∴ Gain = (125000 - 100000) units

= 25000 units.

∴ Gain % = (25000×100)/100000

= (25000/1000)

= 25 %.

∴ The gain of the man is 25 %.

Answer:

His gain is 25%.

Does the triangle inequality hold for the vectors u and v?
u = (2, 0), v = (1, -2)

Answers

For the vectors, u = (2, 0) and v = (1, -2), the triangle-inequality holds True.

In order to determine if triangle-inequality holds for vectors u = (2, 0) and v = (1, -2), we check if the sum of the lengths of two sides of a triangle is greater than or equal to the length of the remaining side.

Let us calculate the lengths of the vectors "u" and "v":

|u| = √(2² + 0²) = √(4) = 2

|v| = √(1² + (-2)²) = √(1 + 4) = √5

Now, we check if the triangle-inequality holds:

|u + v| = |(2, 0) + (1, -2)| = |3, -2| = √(3² + (-2)²) = √(9 + 4) = √13,

According to the triangle inequality, |u + v| ≤ |u| + |v|.

√13 ≤ 2 + √5,

13 ≤ 4 + 2√5 + 5

13 ≤ 9 + 2√5

It is clear that the triangle-inequality holds for given vectors u and v because 13 is less than or equal to 9 + 2√5.

Therefore, the triangle inequality holds for the vectors u = (2, 0) and v = (1, -2).

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The length of a rectangle is three feet less than two times the width. The perimeter is 27 feet. Find the dimensions.​

Answers

Answer:

l = 2w - 3

2(2w - 3) + 2w = 27

4w - 6 + 2w = 27

6w - 6 = 27

6w = 33, so w = 5.5 feet and l = 8 feet

Answer:


Width: 5.5 feet

Length: 8 feet

Step-by-step explanation:

Let's begin by assigning variables to stand in for the rectangle's width and length.


Let x represent the rectangle's width.

The length is three feet shorter than double the width, according to the problem. As a result, the length may be written as:


2x - 3

The lengths of all the sides make up a rectangle's perimeter, which in this instance is:

2w + 2l

By substituting the width and length measurements we discovered:

2x + 2(2x - 3)

Simplifying:


2x + 4x - 6 = 27

6x = 33

x = 5.5

The rectangle is 5.5 feet wide as a result.

We may change x into the expression we discovered earlier to figure out the length:

2(5.5) - 3 = 8

The rectangle is 8 feet long as a result.

As a result, the rectangle's measurements are:

Width: 5.5 feet

Length: 8 feet


Assume that when adults with smartphones are random y selected 53% use the in meeting the probability that fewer than 5 of them use their smartphones in meetings or classes. s or classes. If 11 adult smartphone users are randomly selected,
find The probability is
(Type an integer or decimal rounded to four decimal places as needed.) 

Answers

The probability that fewer than five of the 11 randomly selected adult smartphone users will use their phones during meetings or classes is 0.6747

How do we calculate the probability?

When adults with smartphones are randomly selected, 53% use them during meetings or classes. You need to find the probability that fewer than five of the 11 selected adults use their smartphones during meetings or classes. Here's how to calculate the probability that fewer than five of the 11 randomly selected adult smartphone users will use their phones during meetings or classes:

\(P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)\)

Where X represents the number of smartphone users in the selected group who use their phones in meetings or classes. Using the binomial probability formula, you can calculate each of these probabilities separately.

\(P(X = 0) = (11C0)(0.53)^0(1 - 0.53)^11 = 0.0026\\P(X = 1) = (11C1)( 0.53)^1(1 - 0.53)^10 = 0.0247\\P(X = 2) = (11C2)(0.53)^2(1 - 0.53)^9 = 0.1012\\P(X = 3) = (11C3)(0.53) ^3(1 - 0.53)^8 = 0.2346\\P(X = 4) = (11C4)(0.53)^4(1 - 0.53)^7 = 0.3116\\\)

Therefore, the probability that fewer than five of the 11 randomly selected adult smartphone users will use their phones during meetings or classes is:

\(P(X < 5) = 0.0026 + 0.0247 + 0.1012 + 0.2346 + 0.3116 = 0.6747\)

Therefore, the probability is 0.6747.

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Which of the following equations are equivalent? Select three options. 2 + x = 5 x + 1 = 4 9 + x = 6 x + (negative 4) = 7 Negative 5 + x = negative 2

Answers

Answer:

A. 2 + x = 5

B x + 1 = 4

E -5 + x = -2

Step-by-step explanation:

2 + 3 = 5

3 + 1 + 4

-5 + 3 + -2

if this correct mark me as brainliest please

What is a Normal Probability Plot?

Answers

Answer: The normal probability plot is a graphical technique for assessing whether or not a data set is approximately normally distributed. The data are plotted against a theoretical normal distribution in such a way that the points should form an approximate straight line.

Step-by-step explanation:

The sorted data are shown with an approximation to the means or medians of the associated order statistics to create the normal probability plot.

What is a Normal Probability Plot?

The normal probability plot is a graphical method for determining whether or not a data set is roughly normally distributed . The points in the data are displayed against a hypothetical normal distribution such that they should roughly form a straight line.

The sorted data are shown with an approximation to the means or medians of the associated order statistics to create the normal probability plot. It is applied to ascertain if a tiny amount of data is representative of a normal distribution.

A graphical method for locating significant deviations from normalcy is the normal probability plot. Outliers, skewness, kurtosis, the requirement for transformations, and mixes are some examples of this. The raw data, residuals from model fits, and estimated parameter values are used to create normal probability charts.

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a survey found that 78% of the men questioned preferred computer-assisted instruction to lecture and 68% of the women preferred computer-assisted instruction to lecture. there were 100 randomly selected individuals in each sample. find the 95% confidence interval for the difference of the two proportions.

Answers

The 95% confidence interval for the difference between the two population proportions is -0.022 < p₁ - p₂ < 0.222.

Given that,

In a survey, it was discovered that 68% of women and 78% of men preferred computer-assisted education to lectures, respectively. Each sample contained 100 people that were chosen at random.

We have to calculate the 95% confidence range for the difference between the two proportions.

We know that,

The 95% confidence interval for difference between two population proportions is given as follows :

\(((\bar p_{1} -\bar p_{2})\)±\(Z_{0.05/2}\sqrt{\frac{PQ}{n_{1} } +\frac{PQ}{n_{2} }} })\)

Here,

p₁ is 0.78

p₂ is 0.68

n₁ is 100

n₂ is 100

Z is 1.96

P is 0.73

Q is 0.27

So,

((0.78-0.68)±\(1.96\sqrt{\frac{(0.73)(0.27)}{100 } +\frac{(0.73)(0.27)}{100 }} })\)

(0.10±0.122)

(0.10-0.122,0.10+0.122)

(-0.022,0.222)

Therefore, The 95% confidence interval for the difference between the two population proportions is -0.022 < p₁ - p₂ < 0.222.

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Plywood is sold in 1/4 inch thick sheets that have a length of 8 feet and a width of 4 feet. How many of these sheets will Jill need to cover the floor?

Answers

There are 8 feet³ of these sheets will Jill need to cover the floor.

We have to given that;

Plywood is sold in 1/4 inch thick sheets that have a length of 8 feet and a width of 4 feet.

Hence, The volume of for sheets are,

⇒ 1/4 × 8 × 4

⇒ 8 feet³

Therefore, There are 8 feet³ of these sheets will Jill need to cover the floor.

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Can someone help me understand this I dont understand and I need help

Can someone help me understand this I dont understand and I need help

Answers

I think this is right

Answer:

8 forks

Step-by-step explanation:

12:2

This ratio means there are 12 spoons and 2 forks,

12x4=48 and 2x4=8

48+8=56

Therefore there are 8 forks.

How does graphing two sets of data on one graph help you see patterns?

Answers

Answer:

~Shoto todoroki here~

The Mathematical tables and graphs are a good way to represent patterns. It helps to organize data and can reveal the relationships, making it easier to write equations that describe the patterns.

(Hope this helps!)

And the order goes in

J
K
L
M

please help and don’t just guess and put a wrong answer for points I’m stressed

And the order goes inJKLMplease help and dont just guess and put a wrong answer for points Im stressed

Answers

Answer:

J; (1, -10)

K; (-1, -10)

L; (1,-8)

M; (-1, -8)

Step-by-step explanation:

I double-checked and they are all right. hope this helps!

Find the area of this parallelogram. 9cm 12cm 21cm

Answers

Answer:

2268cm^2

Step-by-step explanation:

Area of a parallelogram is L×B×H

9cm×12cm×21cm= 2268cm^2

Answer:

189

Step-by-step explanation:

B × H =

12× 9 =

= 189 hfjxijdkvkis

3. Which of the following is parallel to the line y = 3/4x +7?

3. Which of the following is parallel to the line y = 3/4x +7?

Answers

The answer would be C. y = 3/4 x - 9

this line has the same slope => ¾

PLEASE !! HELP what is the slope of the line that contains the points ( -2, - 7/2) and (4,-4)

Answers

Answer:   -1/12

Work Shown:

-7/2 = -3.5

The two given points are (-2,-3.5) and (4,-4)

Let's use the slope formula.

\((x_1,y_1) = (-2,-3.5) \text{ and } (x_2,y_2) = (4,-4)\\\\m = \text{slope} = \frac{\text{rise}}{\text{run}} = \frac{\text{change in y}}{\text{change in x}}\\\\m = \frac{\text{y}_{2} - \text{y}_{1}}{\text{x}_{2} - \text{x}_{1}}\\\\m = \frac{-4 - (-3.5)}{4 - (-2)}\\\\m = \frac{-4 + 3.5}{4 + 2}\\\\m = \frac{-0.5}{6}\\\\m = \frac{-1/2}{6}\\\\m = \frac{-1/2}{6/1}\\\\m = \frac{-1}{2}\div\frac{6}{1}\\\\m = \frac{-1}{2}*\frac{1}{6}\\\\m = -\frac{1}{12}\)

The slope is -1/12

It means "go down 1 unit, then go to the right 12 units".

You can use a tool like GeoGebra to confirm the answer is correct.

could you plz help me with this question?​

could you plz help me with this question?

Answers

Answer:

(a) t_n = 3n - 9

(b) t_16 = 39

Step-by-step explanation:

(a)

-3 - (-6) = -3 + 6 = 3

The common difference is 3.

t_1 = -6

t_2 = -6 + 3

t_3 = -6 + 3 + 3

t_4 = -6 + 3 + 3 + 3

t_n = -6 + 3(n - 1)

t_n = -6 + 3n - 3

t_n = -9 + 3n

t_n = 3n - 9

The formula is: t_n = 3n - 9

(b) t_16 = 3(16) - 9 = 48 - 9 = 39

Answer:

an = -6 + 3(n - 1)

a(16) = 39

Step-by-step explanation:

Explicit Formula: an = a1 + d(n - 1)

Our d (common difference) is +3

Our a1 (First term) is -6

To find a(16) (the 16th term), plug in 16 for n.

Describe the graph of y = 1/2 x − 10 − 3 compared to the graph of y = 1 x .

Answers

The graph of y = [1/2(x -10)] - 3, compared to the graph of 1/x, represents these following transformations:

Horizontal compression by a scale factor of 2.Translation right 10 units.Translation down 3 units.

What is a translation?

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The four translation rules for functions are defined as follows:

Translation left a units: f(x + a).Translation right a units: f(x - a).Translation up a units: f(x) + a.Translation down a units: f(x) - a.

The translations for this problem are given as follows:

x -> x - 10: shift right 10 units.y -> y - 3: shift down 3 units.

Additionally, there was a multiplication by 2 in the domain, meaning that the parent function was horizontally compressed by a factor of 2.

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Whats Gibby thinking about

Answers

Answer:

Who is gibby

Step-by-step explanation:

What and who is Gibby ?

Use the graph to answer the question. Graph of polygon ABCDE with vertices at negative 1 comma negative 4, negative 1 comma negative 1, 3 comma negative 1, 3 comma negative 4, 1 comma negative 6. A second polygon A prime B prime C prime D prime E prime with vertices at negative 11 comma negative 4, negative 11 comma negative 1, negative 15 comma negative 1, negative 15 comma negative 4, negative 13 comma negative 6. Determine the line of reflection. Reflection across the x-axis Reflection across x = −6 Reflection across the y-axis Reflection across y = −6 Question 7(Multiple Choice Worth 2 p

Answers

The correct answer is option 1 reflection across the x-axis.

What is a pentagon?

A pentagon is a polygon that consists of five sides and five angles. The total measure of the interior angles of a pentagon is 540 degrees. There are various types of pentagons, such as regular pentagons, where all sides and angles are equal, and irregular pentagons, where sides and angles have different lengths and measures. Pentagons are commonly used in geometry and can be observed in numerous natural and human-made objects, including stars, flowers, architectural and engineering designs, among others.

To determine the line of reflection that maps polygon ABCDE onto polygon A'B'C'D'E', we need to find a line that is equidistant from each corresponding pair of points on the two polygons.

We can see from the graph that the two polygons are mirror images of each other across the x-axis, so the line of reflection is the x-axis.

Therefore, the answer is reflection across the x-axis.

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The complete question is: "Use the graph to answer the question. Graph of polygon ABCDE with vertices at (-1,-4), (-1,-1), (3,-1), (3,-4), (1,-6). A second polygon A' B' C' D' E' with vertices at (-11,-4), (-11,-1), (-15,-1), (-15,-4), (-13,-6). Determine the line of reflection.

1. Reflection across the x-axis

2. Reflection across x = −6

3. Reflection across the y-axis

4. Reflection across y = −6"

Use the graph to answer the question. Graph of polygon ABCDE with vertices at negative 1 comma negative

8) The ball used in a soccer game may not weigh more than 16 ounces or less
than 14 ounces at the start of the match. After 1.5 ounces of air was added to a
ball, the ball was approved for use in a game. Write and solve a compound
inequality to show how much the ball might have weighed before the air was
added.

Answers

The compound inequality for the weight of the ball is represented as 14 > w< 16.

What is inequality?

When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relationship between variables and the numbers.

Given that the ball used in a soccer game may not weigh more than 16 ounces or less than 14 ounces at the start of the match. After 1.5 ounces of air was added to a ball, the ball was approved for use in a game.

The compound inequality will be written as,

14 > w< 16.

Here the weight of the ball varies between 14 ounces to 16 ounces means that the minimum weight should be 14 ounces and the maximum is 16 ounces.

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In the absence of additional information you assume that every person is equally likely to leave the elevator on any floor. What is the probability that on each floor at most 1 person leaves the elevator

Answers

The probability of at most 1 person leaving the elevator on each floor when assuming that every person is equally likely to leave the elevator on any floor depends on the number of floors in the building and can be calculated using the binomial distribution formula.

Assuming that every person is equally likely to leave the elevator on any floor, the probability that on each floor at most 1 person leaves the elevator can be calculated using the binomial distribution.

Let's say there are n floors in the building. The probability of at most 1 person leaving the elevator on each floor is the probability that 0 or 1 person leaves the elevator on each floor. This can be calculated as follows:

P(at most 1 person leaves the elevator on each floor) = P(0 people leave on floor 1) x P(0 or 1 people leave on floor 2) x P(0 or 1 people leave on floor 3) x ... x P(0 or 1 people leave on floor n)

Now, since we are assuming that every person is equally likely to leave the elevator on any floor, the probability of 0 people leaving the elevator on any floor is (n-1)/n and the probability of 1 person leaving the elevator on any floor is 1/n. Therefore, we can calculate the probability of at most 1 person leaving the elevator on each floor as:

P(at most 1 person leaves the elevator on each floor) = (n-1)/n * (1/n + (n-1)/n)^(n-1)

Simplifying this expression, we get:

P(at most 1 person leaves the elevator on each floor) = (n-1)/n * (2/n)^(n-1)

For example, if there are 5 floors in the building, the probability of at most 1 person leaving the elevator on each floor is:

P(at most 1 person leaves the elevator on each floor) = 4/5 * (2/5)^4
P(at most 1 person leaves the elevator on each floor) = 0.08192

Therefore, the probability of at most 1 person leaving the elevator on each floor when assuming that every person is equally likely to leave the elevator on any floor depends on the number of floors in the building and can be calculated using the binomial distribution formula.

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Joan is concerned about the amount of energy she uses to heat her home.
The scatterplot shows the relationship between x = mean temperature in a particular month
and y = mean amount of natural gas used per day (in cubic feet) in that month, along with the regression line y^=1425−19.87x
a. Predict the mean amount of natural gas Joan will use per day in a month with a mean temperature of 30°F

Answers

The predicted mean amount of natural gas Joan will use per day in a month with a mean temperature of 30°F is approximately 828.9 cubic feet.

To predict the mean amount of natural gas Joan will use per day in a month with a mean temperature of 30°F, we will use the given regression line equation: y^ = 1425 - 19.87x.

Step 1: Substitute the value of x (mean temperature) with 30.
y^ = 1425 - 19.87(30)

Step 2: Perform the calculations.
y^ = 1425 - 596.1

Step 3: Simplify the equation.
y^ = 828.9

So, the predicted mean amount of natural gas Joan will use per day in a month with a mean temperature of 30°F is approximately 828.9 cubic feet.

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Tyjae and Jason were asked to find the volume of ball with a diameter of 6 inches. Look at their equations. Who is correct? What mistake did the other person make?

Tyjae and Jason were asked to find the volume of ball with a diameter of 6 inches. Look at their equations.

Answers

I believe it was mark who was wrong because the formula requires you to use the radius squared not the diameter squared

Answer for my problem

Answer for my problem

Answers

The value of the expression 3⁻² is 1 / 9.

The expression given is:

3⁻²

We need to evaluate the expression.

Using the property a⁻² = 1 / a², we get that:

= 1 / 3²

Simplify the expression, we get that:

= 1 / 9.

Therefore, we get that, the value of the expression 3⁻² is 1 / 9.

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(6d+5)−(2−3d) find the difference

Answers

Answer:

9d+7

Step-by-step explanation:

when you subtract you 'add the opposite' so we can rewrite this subtraction problem as an addition problem as follows:

6d + 5 + 2 + 3d

combine 'like' terms to get:

9d + 7

Answer:

3d + 3

Step-by-step explanation:

a survey asked people whether they had ever considered a career in science, and said that they had. can you conclude that the percentage of people who have considered a career in science is more than ? use the level of significance.

Answers

Since our test statistic of 2.727 is greater than the critical value, we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that more than 30% of people have considered a career in science.

To test whether more than 30% of people have considered a career in science, we can use a one-sample proportion hypothesis test. Let p be the true proportion of people who have considered a career in science.

Our null hypothesis is that the true proportion is 0.30 or less, and our alternative hypothesis is that the true proportion is greater than 0.30.

H0: p <= 0.30

Ha: p > 0.30

We can use the sample proportion of 178/514 = 0.346 to estimate the true proportion p. The standard error of the sample proportion is:

√[(0.30 * 0.70) / 514] = 0.022

Using the normal approximation to the binomial distribution, we can calculate the test statistic:

z = (0.346 - 0.30) / 0.022 = 2.727

At the α = 0.05 level of significance, the critical value for a one-tailed test is 1.645.

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Determine if the expression x3y59+y\frac{x^3y^5}{9}+y 9 x 3 y 5 ​ +y is a polynomial or not. If it is a polynomial, state the type and degree of the polynomial.

Answers

The degree of an individual term of a polynomial is the exponent of its variable; the exponents of the terms of this polynomial are, in order, 5, 4, 2, and 7.

The degree of the polynomial is the highest degree of any of the terms; in this case, it is 7.

You may need to use the appropriate appendix table or technology to answer this question.

A population has a mean of 800 and a standard deviation of 200. Suppose a sample of size 400 is selected and

x

is used to estimate μ. (Round your answers to four decimal places.)

(a)____

What is the probability that the sample mean will be within ±5 of the population mean?

(b)___

What is the probability that the sample mean will be within ±10 of the population mean?

Answers

a. The probability that the sample mean will be within ±5 of the population mean is the area under the normal curve between these two z-scores. b. The lower bound z-score is (-10 - 0) / 10 = -1, and the upper bound z-score is (10 - 0) / 10 = 1. We can use the same normal distribution table or technology to find the probability associated with these z-scores.

(a) To find the probability that the sample mean will be within ±5 of the population mean, we can use the Central Limit Theorem (CLT) and the properties of a normal distribution.

The sample mean, is an unbiased estimator of the population mean, μ. According to the CLT, the distribution of sample means approaches a normal distribution with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

     = 200 / √400

     = 200 / 20

     = 10

To find the probability that the sample mean will be within ±5 of the population mean, we can standardize the interval using the z-score:

For the lower bound (-5), the z-score is (-5 - 0) / 10 = -0.5.

For the upper bound (+5), the z-score is (5 - 0) / 10 = 0.5.

We can now use a standard normal distribution table or technology (such as a calculator or statistical software) to find the probability associated with the z-scores -0.5 and 0.5. The probability that the sample mean will be within ±5 of the population mean is the area under the normal curve between these two z-scores.

(b) To find the probability that the sample mean will be within ±10 of the population mean, we follow the same steps as in part (a).

The lower bound z-score is (-10 - 0) / 10 = -1, and the upper bound z-score is (10 - 0) / 10 = 1. We can use the same normal distribution table or technology to find the probability associated with these z-scores.

Note: Since the question mentions rounding answers to four decimal places, please use the appropriate table or technology to obtain the precise probabilities for parts (a) and (b).

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What is the PHP function we used to send an SQL query to a MySQL database, and how would you describe the general form of the return value of this function

Answers

The PHP function commonly used to send an SQL query to a MySQL database is "mysqli_query()." The general form of the return value of this function is a result object, which represents the outcome of the query execution.

In PHP, the "mysqli_query()" function is commonly used to send SQL queries to a MySQL database. It takes two parameters: the first parameter is the database connection object, and the second parameter is the SQL query string. When the "mysqli_query()" function is executed, it sends the SQL query to the MySQL database for execution. The function returns a result object, which represents the outcome of the query execution.

The specific contents of the result object depend on the type of query executed. For SELECT queries, the result object contains the retrieved data from the database, which can be fetched using other functions like "mysqli_fetch_assoc()" or "mysqli_fetch_array()." For INSERT, UPDATE, DELETE, or other types of queries, the result object typically indicates the success or failure of the query execution.

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In Buenos Aires, Argentina, the average monthly temperature is highest in January and lowest in July, ranging from 83°F to 57°F . Write a cosine function that models the change in temperature according to the month of the year.

b. What part of the problem describes the length of the cycle?

Answers

The length of the cycle is one year, or 12 months.

The cosine function that models the change in temperature according to the month of the year in Buenos Aires can be represented as:

T(t) = A * cos((2π/12) * t) + B

Where:

T(t) represents the temperature at a given month t.

A represents the amplitude of the temperature fluctuations, which is half the difference between the highest and lowest temperatures. In this case, A = (83°F - 57°F) / 2 = 13°F.

B represents the average temperature, which is the midpoint between the highest and lowest temperatures. In this case, B = (83°F + 57°F) / 2 = 70°F.

t represents the month of the year, where January is represented by t = 1, February by t = 2, and so on.

The term (2π/12) * t represents the angle in radians that corresponds to the month t. Since there are 12 months in a year, we divide the full circle (2π radians) by 12 to get the angle for each month.

The part of the problem that describes the length of the cycle is the period of the cosine function, which represents the time it takes to complete one full cycle. In this case, the period is 12 months, as it takes one year for the temperatures to go through a complete cycle from the highest point in January to the lowest point in July and back to the highest point again.

Therefore, the length of the cycle is one year, or 12 months.

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