What are the zeros of this function?

Answer:

  (x, y) = (3.4, -0.2)

Step-by-step explanation:

You want a graphical solution for the system of equations ...

The graph and solution are shown in the attachment. A graphing calculator is a nice bit of useful technology for this. The solution is ...

  (x, y) = (3.4, -0.2)

The first line has x-intercept 3 and y-intercept 1.5.

The second line has y-intercept -7 and slope 2. It crosses the x-axis at x=3.5, so will cross the first line in the 4th quadrant.

The z value of 0.2 indicates the standardized difference between the sample mean and population mean

The z value is a standardized score that tells us how many standard deviations a sample mean is from the population mean. In other words, it helps us determine the likelihood that the difference between the two means is due to chance or some other factor.

Typically, we use a significance level (often denoted by alpha) to determine if the z value is significant or not. If the z value falls within the critical values for the chosen significance level, we reject the null hypothesis and conclude that there is a significant difference between the two means. If the z value falls outside the critical values, we fail to reject the null hypothesis and conclude that there is not a significant difference.

In your case, with a z value of 0.2, it is important to consider what significance level was used in the test. If the chosen significance level was 0.05. Since 0.2 falls within this range, we would fail to reject the null hypothesis and conclude that there is not a significant difference between the sample mean and population mean.

To know more about z value here.

https://brainly.com/question/30172182

#SPJ4

The total cost of the cement rings for the water well is RS. 70,000. This cost is only for the cement rings and does not include the cost of labour for digging the well.

The cost of each cement ring is given as RS. 2500. Since there are 28 cement rings used in the water well, the total cost of the cement rings can be calculated as follows:

Total cost of cement rings = Cost of each cement ring x Number of cement rings used

Total cost of cement rings = 28 x 2500 = RS. 70,000

Volume of the well = [tex]\mathrm{ \pi r^2h = \pi (0.7)^2(5.6) = 9.768m^3 }[/tex]

Cost of digging out the well = 500 x 9.798 = RS. 4,899

Total cost of the well = RS. 74,899

Total cost of cement rings = 2500 x 28 = RS. 70,000

Therefore, the total cost of the cement rings for the water well is RS. 70,000. This cost is only for the cement rings and does not include the cost of labour for digging the well.

To know more about Total Cost visit:

brainly.com/question/28652728

#SPJ1

The exponential equation is given by the function y = 30.5(0.7)ˣ

An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.

The standard form of an exponential equation is:

y = abˣ

where b is the rate of change and a is the initial value.

Let y represent the number of games sold x years since 2015.

From the graph, at point (0, 30.5):

30.5 = ab⁰

a = 30.5

Also, at point (1, 21.35):

21.35 = ab¹;     but a = 30.5, hence:

21.35 = 30.5b

b = 0.7

The equation is y = 30.5(0.7)ˣ

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

Given point D is the centroid of triangle ABC, BD = 4x + 2 and DF = 3x and the value of x is -1

Centroid is a term used in triangles and it is equals to the reciprocal of three-second of the distance from each midpoint of the given triangle to each vertices.

Given point D is the centroid of triangle ABC, BD = 4x + 2 and DF = 3x and Centroid is a term used in triangles and it is equals to the reciprocal of three-second of the distance from each midpoint of the given triangle to each vertices.

we know that,

BD = 4x+2

DF = 3x

So by the given formulae, we used to solve the x value as,

BD = (1/(3/2)) [DF]

BD = (2/3)[DF]

4x+2 = (2/3)(3x)

4x+2 = 2(x)

4x+2 = 2x

4x-2x = -2

2x = -2

x = -1

Therefore, the value of x is x = -1

Learn more about centroid here:

https://brainly.com/question/10708357

#SPJ4

If , Pete is saving $0. 45 each week to buy a video game that cost $9.0. Pete will have to save for 20 weeks to have enough money to buy the video game.

The problem asks us to find out how many weeks Pete will have to save to buy a video game that costs $9.0 if he is saving $0.45 each week. To solve this problem, we can use division to find out how many times $0.45 goes into $9.0.

We first divide the total cost of the game by the amount Pete saves each week, which gives us the number of weeks he will need to save.

In this case, the division of $9.0 by $0.45 yields 20, which means that Pete will have to save for 20 weeks to buy the video game. This calculation is important for Pete because it helps him plan his savings and gives him a goal to work towards. By saving $0.45 every week, he can keep track of his progress and stay motivated to reach his goal.

This problem highlights the importance of basic arithmetic skills, specifically division, in practical situations like budgeting and financial planning. By applying mathematical concepts to everyday situations, we can make informed decisions and manage our resources more effectively.

To learn more about price calculation click on,

https://brainly.com/question/14603265

#SPJ4

One gallon is equivalent to 4 quarts, so 1 1/2 gallons is equal to 1 1/2 x 4 = 6 quarts. To determine if the amount of water in the bucket is greater than, less than, or equal to 6 quarts, we need to convert the amount from gallons to quarts.

A gallon is a unit of volume commonly used in the United States, while a quart is a unit of volume commonly used in both the US and the UK.

One gallon is equivalent to 4 quarts, so 1 1/2 gallons is equal to 1 1/2 x 4 = 6 quarts.

Therefore, the amount of water in the bucket is equal to 6 quarts.

It's important to be able to convert between different units of measurement to effectively communicate and understand various quantities. In the case of volume, it's crucial to use consistent units when comparing the amount of liquids in containers or when measuring the volume of substances.

Conversion between units of measurement also plays a significant role in many fields, such as cooking, baking, construction, and engineering, where precise measurements are critical.

In conclusion, the amount of water in the bucket is equal to 6 quarts, and the ability to convert between different units of measurement is an important skill in various areas of life and work.

To know more about A gallon click here:

brainly.com/question/11329119

#SPJ4

Hence, the probability that both defective bulbs will be selected is 0.1630

We are given that a box containing 24 light bulbs. 2 light bulbs are defective.

Now if a person selects 10 bulbs at random, without replacement.

We are required to find the probability that both defective bulbs will be selected.

Since there are two defectives, therefore two defective can be chosen in(2,2) ways.

Also since 10 bulbs are selected, the remaining 8 bulbs can be selected in (22,8)

Also, the total number of ways 10 bulbs can be selected is:

[tex]^{22}C_8\\[/tex]

Therefore, the probability that both defective bulbs will be selected is:

[tex]=\frac{(^2c_2)(^{22}C_2)}{^{24}C_10}\\\\=1.630.[/tex]

rounded to 4 decimal places

Hence, the probability that both defective bulbs will be selected is 0.1630

learn more about Probability,

https://brainly.com/question/30034780

#SPJ4

Since in the figure, a || b and m∠1 = 34°, the magnitude of m∠5 is equal to 34°.

In Mathematics, parallel lines are two lines that are cut through by a transversal and they always have the same (equal) distance apart and never meet.

In Mathematics, corresponding angles can be defined as a postulate (theorem) which states that corresponding angles are always congruent when the transversal intersects two (2) parallel lines. This ultimately implies that, the corresponding angles will be always equal (congruent) when a transversal intersects two (2) parallel lines.

By applying corresponding angles theorem to lines a and b, we have the following:

m∠1 ≅ m∠5

m∠5 = 34°.

Read more on parallel lines here: brainly.com/question/16959398

#SPJ1

The measures of angle possible for of an isosceles triangle when one angle given is 140° then other two angles is 20°.

In an isosceles triangle, two of the angles have the same measure. Let's call this measure x. Since the sum of the angles of a triangle is 180 degrees, we can set up an equation:

x + x + 140° = 180°

Simplifying the equation, we get:

2x + 140° = 180°

Subtracting 140° from both sides, we get:

2x = 40°

Dividing both sides by 2, we get:

x = 20°

So the other two angles in the isosceles triangle each measure:

x = 20°

Therefore, the measures 28°, 22°, 26° are not possible for the other two angles of the isosceles triangle, but the measure 20° degrees is possible.

To Know more about the angles:

https://brainly.com/question/14684647

#SPJ4

The two lines have the same slope and different y-intercepts, thus, the lines are parallel.

Here we want to find the relation between the two lines:

8x = 3y + 3

-24x + 9y = 3

First, we need to write these two as lines in the slope-intercept form. We will get:

3y = 8x - 3

y = (8/3)*x - 3/3

y = (8/3)*x - 1

And the other one:

9y = 3 + 24x

y = (3/9) + (24/9)*x

y = (1/3) + (8/3)*x

So, we can see that both lines have the same slope (and different y-intercept), thus, the lines are parallel lines.

Learn more about linear equations at:

https://brainly.com/question/1884491

#SPJ1

Answer:

27, 36

Explanation:

To find the possible two-digit numbers that meet the criteria, we can use algebra. Let x be the original two-digit number, and let y be the reverse of x. Then, we have:

x - y = 18

We can also write y in terms of x:

y = x % 10 * 10 + x / 10

Substituting the expression for y into the equation x - y = 18, we get:

x - (x % 10 * 10 + x / 10) = 18

Expanding and simplifying the right side of the equation, we get:

9x = 180 + 10

Dividing both sides of the equation by 9, we get:

x = 20

Since x must be a two-digit number, 20 is not a valid solution. However, we can check the two numbers that are close to 20, which are 18 and 21.

For x = 18, we have y = 81, which is a two-digit number, so 18 is a valid solution.

For x = 21, we have y = 12, which is a two-digit number, so 21 is also a valid solution.

Therefore, the possible two-digit numbers that meet the criteria are 27 and 36.

A. The functions are not inverse of each other.

B.  The domain of the composition using interval notation is (-∞, ∞)

Function is a relation between a set of inputs and a set of outputs which are permissible. In a function, for particular values of x we will get only a single image in y. It is denoted by f(x).

A. To show that two functions are inverses of each other, we need to show that their compositions are equal to the identity function, which is denoted as f(x) = x.

That is, we need to show that:

(f ∘ g)(x) = x

(g ∘ f)(x) = x

where ∘ denotes function composition.

First, we'll find the composition (f ∘ g)(x):

(f ∘ g)(x) = f(g(x))

             = f(9x+1)

             = (9x+1) - 3

             = 9x - 2

Next, we'll find the composition (g ∘ f)(x):

(g ∘ f)(x) = g(f(x))

             = g(x-3)

             = 9(x-3) + 1

             = 9x - 26

Since (f ∘ g)(x) ≠ x and (g ∘ f)(x) ≠ x, the functions f(x) and g(x) are not inverses of each other.

B. To find the domain of (f ∘ g)(x), we need to ensure that the input to g(x) is within its domain, which it is for all real numbers. To find the domain of (g ∘ f)(x), we need to ensure that the input to f(x) is within its domain, which it is for all real numbers.

Therefore, the domains of (f ∘ g)(x) and (g ∘ f)(x) are both all real numbers, and we can express this using interval notation as:

Domain of (f ∘ g)(x) and (g ∘ f)(x):

(-∞, ∞)

To know more about Functions check:

https://brainly.com/question/5975436

#SPJ9

(a) The percentage of people that left the event in the afternoon is 8%

(b) The total number of people that were there at the start of the fund-raising event were 68.

Let x be the number of people at the start of the event. Then, 0.6x were males and 0.4x were females.

In the afternoon, 0.2 * 0.4x = 0.08x females left the event.

So, there were 0.4x - 0.08x = 0.32x females left at the event.

In the evening, 33 + 35 = 68 people left the event, and x - 68 people were left.

Out of the x - 68 people, 0.6(x - 68) were males.

So, we have 0.75 * (x - 68) = 0.6 * (x - 68).

We can now solve for x:

0.75 * (x - 68) = 0.6 * (x - 68)

0.15 * (x - 68) = 0

x - 68 = 0

x = 68

Thus, there were 68 people at the start of the fund-raising event.

(a) The percentage of people who left the event in the afternoon was 0.08x / x * 100% = 0.08 * 100% = 8%.

(b) There were 68 people at the start of the fund-raising event.

learn more about percentage: https://brainly.com/question/24877689

#SPJ1

Step-by-step explanation:

Since it varies directly, we can set up a ratio and solve for x

[tex] \frac{ - 4}{ - 2} = \frac{x}{12} [/tex]

Next we would cross multiply... multiply the numbers diagonally

[tex]( - 4)(12) = ( - 2)(x)[/tex]

Simplifying

[tex] - 48 = - 2x[/tex]

Now to get X alone, we would divide by the number attached to it, so -2. We'd do -2 on the -48 also

[tex]x = 24[/tex]

a) The histogram of the data is illustrated below.

b) A cumulative percentage polygon is illustrated on histogram.

c) The cumulative percentage polygon shows us that approximately 66% of calls fall below 240 seconds.

Histograms are a way of representing data visually by dividing it into intervals or bins and plotting the frequency of data points in each bin. In this problem, we will be constructing a percentage histogram and polygon to analyze call duration data.

The call duration data is provided in seconds for 50 customers. To construct a percentage histogram, we need to first determine the bin size or interval. One way to do this is to use the square root rule, which states that the number of bins should be approximately equal to the square root of the sample size. In our case, the sample size is 50, so we can round the square root to 7 and use 7 bins.

Next, we need to determine the range of the data and set the limits for each bin. The range of the data is from 65 to 1141 seconds. We can set the limits for each bin as follows: 60-180, 181-300, 301-420, 421-540, 541-660, 661-780, 781-900, and 901-1020.

To construct the percentage histogram, we need to divide the frequency in each bin by the total sample size and multiply by 100. This gives us the percentage of data points in each bin. We can then plot these percentages as bars of equal width for each bin.

The percentage polygon is constructed by connecting the midpoints of the tops of each bar in the histogram with straight lines. This creates a polygon that represents the distribution of data in the histogram.

In this problem, we are asked to analyze call center performance if a call duration target of less than 240 seconds is set. From the percentage histogram and polygon, we can see that the majority of calls fall within the first three bins, which correspond to call durations of 60-180, 181-300, and 301-420 seconds. Only a small percentage of calls exceed 420 seconds.

To know more about histogram here.

https://brainly.com/question/14421716

#SPJ4

Using an equation, the bride-to-be and her maid of honor will each have made 25 favors in 5 minutes.

An equation is a mathematical statement showing that two or more mathematical expressions are equal or equivalent.

Equations are depicted using the equal symbol (=), while mathematical expressions, which combine variables, constants, and values only use mathematical operands.

The total number of wedding favors assembled by the bride-to-be = 15

The bride's assembling rate per minute = 2 favors

The maid of honor's assembling rate per minute = 5 favors

Let x = the number of minutes used

Let the number of favors assembled by the bride = 15 + 2x

Let the total number of favors assembled by the maid of honor = 5x

For the two to assemble the same number of favors, 15 + 2x = 5x

15 = 3x

5 = x

Thus, in 5 minutes the bride-to-be and her maid of honor will have assembled 25 favors each.

Learn more about equations at https://brainly.com/question/22688504.

#SPJ1

The elevator is on the 14th floor at this situation.

What is the basic arithmetic operation?

Arithmetic operations are mathematical operations that involve basic calculations such as addition, subtraction, multiplication, and division. These operations are used to perform calculations with numbers and are used in a wide range of mathematical and real-life situations.

If the elevator is on the 18th floor, and it moves down 16 floors, it will be on the 2nd floor.

After that, the elevator comes up 12 floors from the 2nd floor. So, it will be on the floor:

2 + 12 = 14

Therefore, the elevator is on the 14th floor at this situation.

To learn more about basic arithmetic operations, visit:

https://brainly.com/question/4721701

#SPJ1

The number line is represented by the inequality -

Option C - |2x - 1| ≥ 9

What is an inequality?

In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.

The number line indicates two filled circles which suggests the inequality contains (≤,≥) symbols and is inclusive of range.

The first inequality will be x ≤ -4 since the value is starting from -4 and moving towards negative infinity.

Similarly, the second inequality will be x ≥ 5 since the value is starting from 5 and moving towards positive infinity.

The compound inequality that results in same is -

|2x - 1| ≥ 9

Apply the absolute rule -

2x - 1 ≥ 9 or 2x - 1 ≤ -9

Solve the inequality -

2x - 1 ≥ 9 or 2x - 1 ≤ -9

2x - 1 + 1 ≥ 9 + 1 or 2x - 1 + 1 ≤ -9 + 1

2x ≥ 10 or 2x ≤ -8

x ≥ 5 or x ≤ -4

Therefore, the inequality is |2x - 1| ≥ 9.

To learn more about inequality from the given link

https://brainly.com/question/11234618

#SPJ1

Answer: To find the total change in pounds of fruit in the basket, we need to subtract the amount taken out from the amount added.

First, let's convert all the fractions to decimals:

1 1/4 = 1.25

2 3/8 = 2.375

Now, we can subtract:

1.25 - 2.375 = -1.125

So, the total change in the fruit basket was -1.125 pounds, meaning the basket had 1.125 pounds less fruit after the removal.

Step-by-step explanation:

The number of green rugs is more than the number of purple rugs. Then the amount of blue rug will be 29/4 square units.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Nina buys a new rug that matches three colors in her bedroom. The rug is a rectangle. There are eight squares on the rug. Four-eighths of the squares are green. One-fourth of the squares are purple.

The amount of green rug is given as,

⇒ 4/8

⇒ 1/2 square units

The amount of purple rug is given as,

⇒ 1/4 square units

The number of green rugs is more than the number of purple rugs.

The amount of blue rug is given as,

⇒ 8 - 1/4 - 4/8

⇒ (64 - 2 - 4) / 8

⇒ 29/4 square units

The number of green rugs is more than the number of purple rugs. Then the amount of blue rug will be 29/4 square units.

More about the Algebra link is given below.

https://brainly.com/question/953809

#SPJ1

In a simple linear regression model we use the normal quantile plot of the residuals to evaluate if it is reasonable to assume the error term come from a normal distribution.

In a simple linear regression model, the normal quantile plot of the residuals is a graphical tool used to assess the normality assumption of the error term (also known as the residual). The error term represents the difference between the actual value of the dependent variable and the predicted value by the model.

Assuming that the error term follows a normal distribution is important for various reasons. Firstly, the normal distribution is a very common assumption in statistics, and many statistical methods rely on it. Secondly, a normal distribution of the error term is essential for making reliable predictions and for computing valid confidence intervals.

The normal quantile plot of the residuals compares the distribution of the residuals against a theoretical normal distribution. The plot consists of a straight line if the residuals are normally distributed. However, if the plot shows deviations from the straight line, it indicates non-normality in the residuals.

If the normality assumption is not satisfied, we need to explore the reasons for the non-normality and consider alternative methods to analyze the data, such as non-parametric methods.

Therefore, the normal quantile plot of residuals is an essential diagnostic tool in simple linear regression, as it allows us to evaluate the assumption of normality and make appropriate adjustments to the model.

To learn more about regression click on,

https://brainly.com/question/30672101

#SPJ4

The formula to describe the variation is F = 1.6d².

Option C is the correct answer.

An equation is made up of one or two variables with a constant connected by an equal sign.

Example:

2x + 4 = 9 is an equation.

We have,

F is directly proportional to the square of d.

This can be written as,

F ∝ d²

F = kd² ____(1)

Now,

F = 40 when d = 5.

40 = k x 5²

k = 40/25

k = 8/5 _____(2)

Now,

From (1) and (2).

F = (8/5)d²

F = 1.6d²

Thus,

The formula to describe the variation is F = 1.6d².

Learn more about equations here:

https://brainly.com/question/17194269

#SPJ1

Step-by-step explanation:

suppose you brought 45 shares of telecommunications company 4 years ago at a price of $63.00 per share. you just sold it for $71.50 per share. how much did you make

Answer:

C. Addition Property of Equality

Step-by-step explanation:

From step 4 to step 5, 20 is added to both sides.

Answer: Addition Property of Equality

She had to pay they have to pay her back $ 132.

Multiply: -

Payback = 360 x 120/100

               = 132

Payback is a financial metric that measures the time it takes to recover the initial investment cost of a project. It is commonly used in investment analysis to evaluate the viability of potential projects by estimating the time it takes for the project to start generating profits.

The payback period is calculated by dividing the initial investment by the expected cash flow of the project on an annual or monthly basis until the investment is fully recovered. The shorter the payback period, the more attractive the project is to investors. Payback is a simple and straightforward metric, but it has some limitations. It does not consider the time value of money or the long-term profitability of the project.

To learn more about Payback visit here:

brainly.com/question/29897703

#SPJ4

Complete Question: -

Paula went to the supermarket and to pay her bill she gave $ 360 if she gave 120% of what she had to pay, how much did they have to pay her back?

Alexandria can expect to spend about $128.25 on school lunches for the year if she forgets to bring her lunch about once a week.

If Alexandria forgets to bring her lunch 15% of the time, then she will need to buy a school lunch on 15% of the 180 school days:

15% of 180 = 0.15 × 180 = 27 school days

So, Alexandria will buy a school lunch 27 times during the school year.

The average cost of a school lunch is $4.75.

So the total cost of buying school lunches for the year will be:

27 × $4.75 = $128.25

Therefore, Alexandria can expect to spend about $128.25

Learn more about average cost here

brainly.com/question/13029865

#SPJ4

The answer is that there is no probability for this event to happen. To find the probability of getting exactly one red marble or exactly one green marble and not both at the same time, we can use the following steps:

Step 1: Find the number of ways to draw 3 marbles out of 12.

This can be found using the combination formula, which gives:

C(12,3) = 12! / (3! * 9!) = 220

Therefore, there are 220 ways to draw 3 marbles out of 12.

Step 2: Find the number of ways to draw exactly one red marble and two non-red marbles.

There are 3 red marbles, and we need to choose one, so there are C(3,1) = 3 ways to do this. There are 9 non-red marbles, and we need to choose two of them, so there are C(9,2) = 36 ways to do this. Therefore, 3 * 36 = 108 ways to draw exactly one red marble and two non-red marbles.

Step 3: Find the number of ways to draw exactly one green marble and two non-green marbles.

There are 4 green marbles, and we need to choose one, so there are C(4,1) = 4 ways to do this. There are 8 non-green marbles, and we need to choose two of them, so there are C(8,2) = 28 ways to do this. Therefore, there are 4 * 28 = 112 ways to draw exactly one green marble and two non-green marbles.

Step 4: Find the number of ways to draw exactly one red marble and one green marble. There are 3 red marbles and 4 green marbles, and we need to choose one of each, so there are 3 * 4 = 12 ways to do this.

Step 5: Add the results from steps 2, 3, and 4 to get the number of ways to draw marbles that satisfy the given condition.

Total number of ways = 108 + 112 + 12 = 232

Step 6: Find the probability of getting exactly one red marble or one green marble but not both at the same time.

The probability of an event is the number of ways that event can happen divided by the total number of possible outcomes. Therefore, the probability of getting exactly one red marble or exactly one green marble and not both at the same time is:

P = (number of ways to draw marbles that satisfy the given condition) / (total number of ways to draw 3 marbles out of 12 marbles)

P = 232 / 220

P = 1.0545

However, probabilities cannot be greater than 1. Therefore, the answer is that there is no probability for this event to happen.

To learn more probabilities, visit here

https://brainly.com/question/29251028

#SPJ4

Answer:

C.

Step-by-step explanation:

area = length × width

5/8 = 1/6 × w

w = (5/8) / (1/6)

Answer: C.