Course activity: modeling with functions

Monica and Shanna are saving the money they earn from their after-school jobs to go on a school trip. Monica starts with $20 and then saves $14 each week. Shanna's savings are shown in the table.

Monica’s savings can he modeled by a ____ table
Shanna’s savings can be modeled by a ____ table

Figure C is the only angle that falls within the Range of 91 to 179 degrees.

An obtuse angle is an angle that measures between 91 and 179 degrees. Therefore, the correct answer is (c) Figure C. An obtuse angle is larger than a right angle (90 degrees) and smaller than a straight angle (180 degrees).

Figure A is a right angle measuring 90 degrees, which is smaller than an obtuse angle. Figure B is an acute angle measuring less than 90 degrees, which is also smaller than an obtuse angle. Figure D is a straight angle measuring 180 degrees, which is larger than an obtuse angle.

Figure C is the only angle that falls within the range of 91 to 179 degrees, making it the correct answer to the question.

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So,

First, remember that:

Given a function f(x). If we make the following changes to it (where c is a number), they will represent:

1. Horizontal translation.

The expression above represents a horizontal translation.

So, if we have f (x - 3) this is a horizontal translation 3 units to the right.

If the sign is positive, the graph moves to the left and if it's negative, it moves to the right.

2. Vertical translation:

The expression above represents a vertical translation.

So, if we have f(x) + 2, this change represents a vertical translation 2 units up.

If the sign is positive, the graph moves c units up, and if it is negative, the graph moves c units down.

3. X-axis reflection.

The expression above represents a X-axis reflection.

So, given -f(x), that's a reflection over the x-axis.

4. y-axis reflection.

The expression above represents a y-axis reflection.

So, given f(-x), that's a reflection over the y-axis.

5. Horizontal compression:

If |c| is greater than 1, this is a horizontal compression.

If |c| is between 0 and 1, this is a horizontal stretch.

In our problem, we are given f(3x), and, as 3 is greater than 1, we have a horizontal compression.

6. Vertical stretch:

If |c| is greater than 1, this is a horizontal compression.

If |c| is between 0 and 1, this is a horizontal stretch.

The  distance between the shortstop and the pitcher calculated as per the given data is 63.6.

Distance between two consecutive bases = 90 feet

Halfway distance between them will be = 45 feets

therefore, halfway distance between first base and second base = 45 feet

and that between second base and third base = 45 feet

So the distance between the  shortstop and the pitcher using pythagoras theorem

= >SP² = PQ² + QS²

           = 45²  + 45²

            =4050

SP = 63.6

Therefore , the required distance is 63.36feets.

The Pythagorean Theorem, often known as Pythagoras Theorem, is a crucial concept in mathematics that describes how the sides of a right-angled triangle relate to one another. Pythagorean triples are another name for the sides of the right triangle

In essence, the Pythagorean theorem is used to determine a triangle's angle and length of an unknown side. We can derive the base, perpendicular, and hypotenuse formulas using this theorem.

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If 7/9 of the box is green counters, and there are 24 yellow counters in the box, then there are 84 green counters .

Let's assume that the total number of counters in the box is x.

We are given that 7/9 of the box is filled with green counters, which means that the remaining 2/9 of the box must be filled with yellow counters. We are also given that there are 24 yellow counters in the box.

We can set up an equation to represent the relationship between the number of yellow counters and the total number of counters:

2/9 x = 24

To solve for x, we can multiply both sides of the equation by the reciprocal of 2/9, which is 9/2:

(2/9) x * (9/2) = 24 * (9/2)

x = 108

This means that there are a total of 108 counters in the box. To find out how many of these are green counters, we can use the fact that 7/9 of the box is filled with green counters:

(7/9) * 108 = 84

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Answer:

t₉ = 32805

Step-by-step explanation:

The nth term of a geometric sequence is

\(t_{n}\) = t₁ \((r)^{n-1}\)

Here t₁ = 5 and r = - 3 , then

t₉ = 5 \((-3)^{8}\) = 5 × 6561 = 32805

The highest point on the graph of the normal density curve is located at its mean represented by μ.

The highest point on the graph of the normal density curve is located at its mean. The normal density curve or the normal distribution is a bell-shaped curve that is symmetric about its mean. The mean of a normal distribution is the measure of the central location of its data and it is represented by μ. It is also the balancing point of the distribution. In a normal distribution, the standard deviation (σ) is the measure of how spread out the data is from its mean.

It is the square root of the variance and it determines the shape of the normal distribution. The normal distribution is an important probability distribution used in statistics because of its properties. It is commonly used to represent real-life variables such as height, weight, IQ scores, and test scores.

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Answer:

the answer I got is x>1-y

The probability of the spinner landing on the letter C is 1/4

To understand the probability of the spinner landing on the letter C, we need to start by looking at the total number of possible outcomes. In this case, there are four possible outcomes, corresponding to the four letters A, B, C, and D.

Since each of the four quadrants on the spinner is equal in size, each of the four letters has an equal chance of being landed on. Therefore, the probability of the spinner landing on the letter C is the number of ways that the spinner can land on C, divided by the total number of possible outcomes.

Since there is only one way for the spinner to land on C, and there are four possible outcomes in total, the probability of the spinner landing on the letter C is 1/4

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The given question is incomplete, the complete question is:

A spinner with four equal quadrants labeled A, B, C, and D is spun. What is the theoretical probability of the spinner landing on the letter C

The conversion 336g to m³ is impossible because they measure different units

From the question, we have the following parameters that can be used in our computation:

Convert 336g to m³

To convert a unit to another, the units must measure the same quantity

Take for instance:

Grams can be converted to kilograms because they both measure mass

Using the above as a guide, we have the following:

336g to m³  cannot be done because of the different quantities they represent

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Answer:

22 feet

Step-by-step explanation:

Answer:The guy is correct. its 2021 eduinty

Have a great day!

Step-by-step explanation:

The maximum volume of his box is approximately 15.

The maximum value of a graph that represents a function is the y-value of the vertex of the parabola, that is, the point where the graph begins to shift from increasing to decreasing.

Thus, in the graph given, the volume is plotted on the y-axis. The graph also shows a parabola that has a vertex at y = 15. This represents the maximum value.

The vertex, which is at y = 15, represents the maximum volume of the box.

Therefore, this means that the maximum volume of his box is approximately 15.

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The equation in the vertex form will be y = (x + b/2a)² - b²/4a² + c/a and the equation in the standard form will be ax² + bx + c = 0.

The quadratic equation is given as ax² + bx + c = 0. Then the degree of the equation will be 2.

Convert the standard equation into a vertex form, then we have

x² + (b/a)x + (c/a) = 0

x² + (b/a)x + b²/4a² - b²/4a² + c/a = 0

(x + b/2a)² - b²/4a² + c/a = 0

Put h = - b/2a and k = - b²/4a² + c/a, where (h, k) be the vertex of the parabola. Then the equation will be

(x - h)² + k = 0

The function written in vertex form will be y = (x - h)² + k and in the standard form will be ax² + bx + c = 0.

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answer is  y=x+216 and -6.

In the question, the expression is given 221--x-5=y;(9-11)3

An equation is said to be linear equation in two variables if it is in the form of ax + by + c=0, where a, b & c are real numbers and  a and b respectively, are not equal to zero. For example, 10x+4y = 3 and -x+5y = 2 are linear equations in two variables.

Unique Solution:

For the given linear equations in two variables, the solution will be unique , if and only if they intersect at a point.

No Solution:

For the given linear equations in two variables, the given system of equations has no solution if lines of two linear equations are parallel.

Infinitely many solution:

For the given linear equations in two variables, the given system of equations has infinitely many solution if lines of two linear equations coincident.

Two consecutive minus signs have the same mathematical meaning as a single plus sign .

221+x-5=y,(9-11).3

x+216=y

Subtract 216 from both sides of the equation,

x+216-216=y-216

x=y-216

replace x with y-216 in the expression

(9-11).3

subtract 11 from 9

-2.3

Multiply -2 by 3

-6

Hence, Final answer is y=x+216 and -6.

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The amount that Susan actually have to pay should be considered as the $1,332.

Since the purchase price of the computer is $1,200

And, the sales tax rate is 11%

So here the total amount be like

= $1,200 + 11% of $1,200

= $1,200 + $132

= $1,332

hence, The amount that Susan actually have to pay should be considered as the $1,332.

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Using the segment addition postulate, we can find that the value of x is 18.

Explanation: The segment addition postulate states that for three points A, B, and C on a line, if B is between A and C, then AB + BC = AC. In this case, we have three points on a line: E, F, and G, and we are given the lengths of two line segments, EF and FG. Using the segment addition postulate, we can set up the following equation:

EF + FG = EG

Substituting the given values, we get:

(7x+9) + (3x+4) = 143

Simplifying the equation, we get:

10x + 13 = 143

Subtracting 13 from both sides, we get:

10x = 130

Dividing both sides by 10, we get:

x = 13

Therefore, the value of x is 13.

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Answer:

3.64 for 13 candy bars

Step-by-step explanation:

The distance apart of the two guy wire is 187.7 metres

The distance apart of the two wires can be found using trigonometric ratios.

Therefore,

tan ∅ = opposite / adjacent

Therefore,

tan 13 = 27 / x

x = 27 / tan 13 = 27 / 0.23086819112 = 117.391304348

tan 21 = 27 / y

y = 27 / tan 21

y = 70.338144115

Therefore,

distance apart of the guy wire = 117.391304348 + 70.338144115 = 187.728144115 = 187.7 metres

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Answer:

The answers is coefficient

Step-by-step explanation:

they both have a variable attached which makes them both coefficients

If the p-value is greater than or equal to the significance level, we fail to reject the null hypothesis and conclude that there is no significant association, found using the chi-square test of independence.

To test whether responses to the satisfaction variable are independent of those who visit the facility daily and those who don't visit daily, we can use the chi-square test of independence. This test assesses whether there is a significant association between two categorical variables.

Here's how you can perform the test in Excel:

1. Set up your data in a table with two columns: "Visit Frequency" and "Satisfaction". Enter the respective frequencies in each category of visit frequency.

2. Calculate the expected frequencies for each combination of visit frequency and satisfaction. To do this, you can use the formula: (row total x column total) / total sample size.

For example, the expected frequency for the combination "Daily" and "Satisfaction" can be calculated as (62 x 25) / total sample size.

3. Calculate the chi-square statistic. In Excel, you can use the CHISQ.TEST function to obtain the chi-square statistic and the associated p-value.

Select a significance level of 10% (0.1) for this test.

4. Interpret the results. If the p-value is less than the significance level (0.1), we reject the null hypothesis of independence and conclude that there is a significant association between visit frequency and satisfaction.

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Answer:

-72

Step-by-step explanation:

-9 * 8 = -72

Hope this helps

Pls mark brainlesit

Answer:

n=12

m=5

Step-by-step explanation:

The sides on the left and right are equal, and the sides on the top and bottom are equal.

Left and right: n=12

Top and bottom: m+1=6; subtract 1 on both sides to get m=5

The number of cast members are in the play given the equation is 16 cast members

7(210 – c) = 1,358

where,

7(210 – c) = 1,358

open parenthesis

1,470 - 7c = 1,358

Subtract 1,470 from both sides

- 7c = 1,358 - 1,470

- 7c = -112

divide both sides of by -7

c = -112 / -7

c = 16

Therefore, there are 16 cast members in the play.

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(a) The distribution of X is binomial with parameters n = 20 and p = 600/3000 = 1/5 since we are randomly selecting 20 clients without replacement and interested in the proportion of happy consumers. Given below is the probability density function for this binomial distribution.

f(x) is equal to (n pick x) * p * x * (1-p) (n-x)

Where p and 1-p are the probability of success and failure, respectively, and n pick x is the binomial coefficient, which is equal to n!/(x! * (n-x)!).

(b) The formula for the anticipated value of X, or E[X], is

E[X] = np = 20 * (1/5) = 4

Var X, the variance of X, is defined as follows:

Var X = np(1-p) = 20*1/5*4/5=3.2

(c) The cumulative distribution function of the binomial distribution's formula can be used to get P[X >= 3]:

Sum(i=3 to n) f for P[X >= 3] (i)

Summarizing from I = 3 to 20 and substituting the values from the density function, we obtain:

Sum(i=3 to 20) = P[X >= 3] [(20 pick I (1/5)*i*4/5*(20-i)]

(d) We must determine the value of the cumulative distribution function at x = 3, which is equivalent to the likelihood of receiving three or fewer successes out of 20 trials, in order to approximate P[X >= 3] using the binomial table. By using n = 20 and p = 1/5 to calculate the value of the cumulative distribution function at x = 3 in the binomial table, it is possible to determine this probability. P[X >= 3]'s estimated value is 0.586.

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Answer:

true

depending on how complete the table of values is.

1000 hours in day can be converted in to by a formula dividing the the 1000 hours by 24 is 41.66 days.

Unit conversion is the process of converting the measurement of a given amount between various units, often by multiplicative conversion factors that alter the value of the measured quantity without altering its effects.

As 1 Hour is equal to 0.0416666666667 Days, you must multiply 1000 by 0.041666666666667 to convert hours to days. The outcome is as follows:

1000 hr × 0.041666666666667 = 41.667 d

1000 hr = 41.667 d

We come to the conclusion that one thousand thousand hours is equal to 41.7667 days:

41.667 days are equivalent to 1000 hours.

Hence, using the conversion method above, you can figure out how many days there are in 1000 hours.

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The area of the branch not covered by the honeycombs is 642.69 square mm

From the question, we have the following parameters that can be used in our computation:

Circle; Radius, r = 14.4 mm

Hexagon; Side length, l = 1.8 mm

The area of the branch not covered by the honeycombs is calculated as

Area = Circle area - Hexagon area

Using the area formulas, we have

Area = 3.14 * 14.4 * 14.4 - 1.5 * √3 * 1.8 * 1.8

Evaluate the products

Area = 651.11 - 8.42

Evaluate the difference

Area = 642.69

Hence, the area of the branch not covered by the honeycombs is 642.69 square mm

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Answer:

63

Step-by-step explanation:

multiply 7 by 18 7 × 18=126 then divide by 2 126÷2=63

When 25 samples are taken to check the claim that 0.70 of item advertised is sold in a week and found 14 to be in favour, performing hypothesis test in a significance level of 5%, we can accept the claim.

A local newspaper claims that 70% of the items advertised in its classifieds section are sold within 1 week, therefore the null hypothesis is

H0 : Probability of items sold within 1 week of advertisement = 0.70

And therefore, H1 : Probability of items sold within 1 week of advertisement ≠ 0.70

p^ = x/ n = 14/ 25 = 0.56

Value np0 and n(1 - p0) is greater than 5, therefore z-statistic can be obtained by z = (x - np0)/ √(np0 × (1 - p0))

z = (14 - 25 × 0.70)/ √(25 × 0.70 × (1 - 0.70))

z = -1.53

p-value = 2 × Ф(−|z|)

≈ 2 × 0.06

= 0.12

As p^ < p0,

p-value = 2 × P(X ≤ x) = 2 × P(X ≤ 14)

We perform the test at a 5% significance level, therefore α = 0.05. Thus, zα/2 = 1.96.

So |z| < zα/2, so we can accept the null hypothesis.

--There are some errors in the question, the correct question is as follows --"A local newspaper claims that 70% of the items advertised in its classifieds section are sold within 1 week of the first appearance of the ad. To check the validity of the claim, the newspaper randomly selected n = 25 advertisements from last year's classifieds and contacted the people who placed the ads. They found that 14 of the 25 items sold within a week. Based on the newspaper's claim, is it likely to observe x < 14 who sold their item within a week? Use a binomial probability table."

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The slope-intercept form of the linear function x - 3y = 18 is given as follows:

y = x/3 - 6.

The slope-intercept representation of a linear function is given as follows:

y = mx + b

The coefficients of the function are described as follows:

In this problem, the equation is given as follows:

x - 3y = 18.

To write the equation in slope-intercept form, we have to isolate the variable y, hence:

3y = x - 18

y = x/3 - 18/3 (divide by 3 to isolate x).

y = x/3 - 6.

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The probability that the mean number of lightning strikes per square kilometer is less than 5 is 0.0016, when  open ground in a year has mean 6 and standard deviation 2.4.

It imply a quantity that falls somewhere between the values of the extreme members of a set in mathematics. There are different types of means, and how they are calculated relies on the relationship that is known about or is regarded as governing the other members.

Given,

Mean = 6

Standard deviation = 2.4

The value that has been reduced by the population mean and divided by the standard deviation is called the z-value.

z = x - mean/ standard deviation/√n

z = 5 - 6/2.4/√50

z = - 2.95

Using table A, calculate the corresponding probability;

= P(x <5)

= P( z < -2.95)

= 0.0016

The probability that the mean number of lightning strikes per square kilometer is less than 5 is 0.0016.

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