a cell phone company offers two texting plans. people who use plan a pay 10 cents for each text sent or received. people who use plan b pay 12 dollars per month, and then pay an additional 2 cents for each text sent or received. write an inequality to represent the fact that it is cheaper for someone to use plan a than plan b. use to represent the number of texts they send. a cell phone company offers two texting plans. people who use plan a pay 10 cents for each text sent or received. people who use plan b pay 12 dollars per month, and then pay an additional 2 cents for each text sent or received. write an inequality to represent the fact that it is cheaper for someone to use plan a than plan b. use to represent the number of texts they send.

Torsion refers to the twisting of a structural member due to the application of torque. Pure torsion occurs when a structural member is subjected to torsional loading only. It is analyzed using assumptions such as linear elasticity, circular cross-sections, and small deformations. The torsion equation relates the applied torque, the polar moment of inertia, and the twist angle of the member. However, this formula has limitations in cases of non-circular cross-sections, material non-linearity, and large deformations.

Torsion is the deformation that occurs in a structural member when torque is applied, causing it to twist. In pure torsion, the member experiences torsional loading without any other external forces or moments acting on it. This idealized scenario allows for simplified analysis and calculations. The assumptions made in pure torsion analysis include linear elasticity, which assumes the material behaves elastically, circular cross-sections, which simplifies the geometry, and small deformations, where the twist angle remains small enough for linear relationships to hold.

To analyze pure torsion, engineers use the torsion equation, also known as the Saint-Venant's torsion equation. This equation relates the applied torque (T), the polar moment of inertia (J), and the twist angle (θ) of the member. The torsion equation is given as T = G * J * (dθ/dr), where G is the shear modulus of elasticity, J is the polar moment of inertia of the cross-section, and (dθ/dr) represents the rate of twist along the length of the member.

However, the torsion equation has its limitations. It assumes circular cross-sections, which may not accurately represent the geometry of some structural members. Non-circular cross-sections require more complex calculations using numerical methods or specialized formulas. Additionally, the torsion equation assumes linear elasticity, disregarding material non-linearity, such as plastic deformation. It also assumes small deformations, neglecting cases where the twist angle becomes significant, requiring the consideration of non-linear relationships. Therefore, in practical applications involving non-circular cross-sections, material non-linearity, or large deformations, more advanced analysis techniques and formulas must be employed.

To learn more about torsion click here: brainly.com/question/30612977

#SPJ11

By applying the definitions of rigid transformation ((x, y) → (0.5 · x, 0.5 · y)) and dilation, we conclude that the coordinates of Q'(x, y) are (0.1).

Herein we must apply a rigid transformation into a given point to determine an image. Rigid transformations are transformations applied on a geometric locus such that Euclidean distance is conserved. Dilations are a kind of rigid transformations such that:

(x, y) → (k · x, k · y), for k > 0

If we know that Q(x, y) = (0, 2) and k = 0.5, then the coordinates of Q' are:

Q'(x, y) = (0.5 · 0, 0.5 · 2)

Q'(x, y) = (0, 1)

By applying the definitions of rigid transformation ((x, y) → (0.5 · x, 0.5 · y)) and dilation, we conclude that the coordinates of Q'(x, y) are (0.1).

To learn more on dilations: https://brainly.com/question/13176891

#SPJ1

Answer: Q' = (0,1)

Step-by-step explanation: just did it on edge

We need a minimum sample size of 336 to estimate the population proportion of U.S. adults who eat fast food four to six times per week with a 90% confidence level.

A) When there is no preliminary estimate available, we can use the worst-case scenario, which is p = 0.5 (since this gives the maximum possible variability). The margin of error is given as 3% or 0.03. The formula to calculate the minimum sample size needed is:

n = [Z² x p x (1 - p)] / E²

where Z is the z-value for the desired confidence level, p is the population proportion, and E is the margin of error.

At 90% confidence, the z-value is 1.645. Plugging in the values, we get:

n = [(1.645)² x 0.5 x (1 - 0.5)] / (0.03)²

n ≈ 1217.75

We need a minimum sample size of 1218 to estimate the population proportion of U.S. adults who eat fast food four to six times per week with a 90% confidence level and an accuracy of 3%.

B) If a proper study found that 11% of U.S. adults eat fast food four to six times per week, we can use this as a preliminary estimate and calculate the minimum sample size needed with the formula:

n = [Z² x p x (1 - p)] / E²

where p is the preliminary estimate of the population proportion (0.11), and the other variables are the same as before.

At 90% confidence, the z-value is 1.645. Plugging in the values, we get:

n = [(1.645)² x 0.11 x (1 - 0.11)] / (0.03)²

n ≈ 335.77

To know more about confidence level, refer:

https://brainly.com/question/20164553

#SPJ4

For any given event, the probability of that event and the probability of the non-occurrence of the event must sum to one.

A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.

The probability of occurrence formula, also known to some as the “probability of occurrence formula PMP” is a tool for determining the chance that a given risk will occur. The formula requires two data points: number of favourable events possible and the total number of events possible.

Non occurrence patterns identifies the absence of events when detecting a pattern.

To know more about probability

https://brainly.com/question/30034780

#SPJ4

Answer:

28

Step-by-step explanation:

You can split the figure up

3*4/2 = 6

3*4/2 = 6

8*2 = 16

6+6+16 = 28

After 3.5 minutes time the car and scooter be in the same position.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The car and scooter are moving at constants speeds.

And, The time, ‘t’ , when they will be in the same position is represented by,

⇒ 21t = 19t + 7

Now, We can solve the expression for time t as;

⇒ 21t = 19t + 7

Subtract 19t both side,

⇒ 21t - 19t = 19t + 7 - 19t

⇒ 2t = 7

⇒ t = 3.5

Therefore, After 3.5 minutes time the car and scooter be in the same position.

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ9

Rebecca needs 6 \( \frac{1}{4} \) more yards of fabric to make the quilt.

Firstly calculating the fabric available to Rebecca = 2 \( \frac{1}{2} \) + 4 \( \frac{1}{4} \)

Fabric available to Rebecca = 5/2 + 17/4

Taking LCM we get 4

Fabric available to Rebecca = 10 + 17/4

Fabric available to Rebecca = 27/4

Let the required fabric be x. So,

17/4 + x = 21/2

x = 21/2 - 17/4

Performing subtraction

Taking LCM we get 4

x = 42 - 17/4

x = 25/4

Converting it back into mixed fraction -

x = 6 \( \frac{1}{4} \)

Thus, the required fabric is 6 \( \frac{1}{4} \) yards.

Learn more about fractions -

https://brainly.com/question/17220365

#SPJ4

The complete question is -

Rebecca needs 10 1/2 yards of fabric to make a quilt. She has one piece of fabric that is 2 1/2 yards and another piece of fabric that is 4 1/4 yards. How many more yards of fabric does Rebecca need to make a quilt.

1) Since this investment has been in an account with 12% compound interest per year, then we can write out the following:

a) Note that there was no withdrawal during this first year.

b) To find out the amount of money over a course of this time 2 years, then we can write out the following:

In this case, it is also compounded per year. Just the period (t) is greater than the other one.

So, we can tell the following about the earnings of this investment:

Answer and Step-by-step explanation:

THE QUESTION IS NOT FROM A QUIZ, IT IS FROM A HOMEWORK ASSIGNMENT.

The unit rate is D. $4.00 per pound.

This is because we see on the graph that at 1 pound of fudge, the cost is 4 dollars.

When looking at the unit rate, you want to look at y value for when x is 1.

#teamtrees #PAW (Plant And Water)

There are 128 four-digit numbers that satisfy the given conditions (exactly one digit 3 and exactly one digit 7, with 7 appearing before 3).

To determine the number of 4-digit numbers that satisfy the given conditions (exactly one digit 3 and exactly one digit 7 with 7 appearing before 3), we can break down the problem step by step.

Step 1: Choose the positions of 3 and 7.

Since 7 must appear before 3, we have two possible cases:

Case 1: 7 is in the thousands place, and 3 is in the hundreds place.

Case 2: 7 is in the hundreds place, and 3 is in the thousands place.

Step 2: Determine the digits in the remaining two positions.

In the remaining two positions (tens and units place), we have eight possible digits to choose from (0, 1, 2, 4, 5, 6, 8, 9). This is because we have used the digits 3 and 7, leaving eight options for the remaining two positions.

Step 3: Calculate the total number of valid numbers.

For each case in Step 1, we multiply the number of choices from Step 2 to get the total count.

Case 1: 7 in thousands place, 3 in hundreds place.

In this case, we have 8 choices for the tens place and 8 choices for the units place. The total count for Case 1 is 8 * 8 = 64.

Case 2: 7 in hundreds place, 3 in thousands place.

Similarly, we have 8 choices for the tens place and 8 choices for the units place. The total count for Case 2 is also 8 * 8 = 64.

Step 4: Sum up the counts from both cases.

To get the final answer, we sum up the counts from both cases:

64 (Case 1) + 64 (Case 2) = 128.

Therefore, there are 128 four-digit numbers that satisfy the given conditions (exactly one digit 3 and exactly one digit 7, with 7 appearing before 3).

To know more about digits , refer here :

https://brainly.com/question/30142622#

#SPJ11

The value of the segment YZ for the similar triangles is equal to 12.5.

The triangles XYZ and WYV are similar, this implies that the length YZ of the smaller triangle is similar to the length YV of the larger triangle

and the length YZ of the smaller triangle is similar to the length YW of the larger triangle

so;

YZ/(5 + YZ) = 10/14

14YZ = 10(5 + YZ) {cross multiplication}

14YZ = 50 + 10YZ

14YZ - 10YZ = 50 {collect like terms}

4YZ = 50

YZ = 50/4 {divide through by 4}

YZ = 12.5

Therefore, the value of the segment YZ for the similar triangles is equal to 12.5.

Know more about similar triangles here:https://brainly.com/question/14285697

#SPJ1

Answer:

8y(7x^3-4x+2)

Step-by-step explanation:

Group and factor out the greastest common factor then combine

Answer:

this is my alt here ya go champ

Step-by-step explanation:

Answer:

x = 66

Step-by-step explanation:

m<5 + m<6 = 180

2x + 48 = 180

2x = 132

x = 66

The maximum difference between Group 1 and Group 2, in the absence of a true difference, depends on the variances, sizes, and mean difference between the groups. Larger variances and sample sizes increase the potential difference, while smaller variances and sample sizes decrease it. A larger mean difference between the groups will result in a larger maximum difference.

The maximum difference between Group 1 and Group 2 that can occur when there is no true difference between the two groups is influenced by several factors. Firstly, the variances of Group 1 and Group 2 play a crucial role.

If the variances are large, it indicates a greater spread of data within each group, which can result in larger differences between individual data points. On the other hand, if the variances are small, the data points tend to be closer together, resulting in smaller differences between them.

Secondly, the sizes of Group 1 and Group 2 also impact the maximum difference between the two groups. When the sample sizes are small, there is a higher chance of observing larger differences by chance alone. Conversely, larger sample sizes tend to provide more reliable estimates and reduce the likelihood of large differences occurring by random variation.

Finally, the difference between the means of Group 1 and Group 2 affects the maximum difference between the groups. A larger difference between the means of the groups will naturally result in a larger maximum difference between individual data points.

In conclusion, the maximum difference between Group 1 and Group 2 that is likely to occur in the absence of a true difference between the groups depends on the variances, sizes, and the difference between their means. By considering these factors, researchers can better understand the expected range of differences that may arise due to random variation and make informed interpretations of their data.

Lean more about variances here:

https://brainly.com/question/20038903

#SPJ11

#43

So

200/2=100 pairs of 201

Sum

#44

400/2=200 pairs of 401

Sum

#45

800/2=400 pairs of 801

Sum

#46

2000/2=1000 pairs of 2001

Sum

Answer:

43.  20,100

44.  80,200

45.  320,400

46.  2,001,000

Step-by-step explanation:

Gauss's method

General formula for the sum of the first n integers:

\(1+2+3+ \dots +n=\dfrac{1}{2}n(n+1)\)

Question 43

Given sum:  

Therefore, n = 200.

Substitute the value of n into the formula:

\(\implies \dfrac{1}{2}(200)(200+1)=100 \cdot 201=20100\)

Question 44

Given sum:  

Therefore, n = 400.

Substitute the value of n into the formula:

\(\implies \dfrac{1}{2}(400)(400+1)=200 \cdot 401=80200\)

Question 45

Given sum:  

Therefore, n = 800.

Substitute the value of n into the formula:

\(\implies \dfrac{1}{2}(800)(800+1)=400 \cdot 801 =320400\)

Question 46

Given sum:  

Therefore, n = 2000.

Substitute the value of n into the formula:

\(\implies \dfrac{1}{2}(2000)(2000+1)=1000 \cdot 2001=2001000\)

Step-by-step explanation:

when you do an arithmetic operation to functions, you do it for the defining expressions.

so,

(f+g)(x) = (x + 3) + (4x + 4) = x + 3 + 4x + 4 = 5x + 7

(f*g)(x) = (x+3)*(4x+4) = 4x² + 12x + 4x + 12 = 4x² + 16x + 12

= 4(x² + 4x + 3)

(f-g)(4) = (4+3) - (4×4+4) = 7 - (16+4) = 7 - 20 = -13

The least number of people we need to select so that the probability is at least 0.6 that at least one person shares our birthday is 24 people.

(a) An expression in terms of n for the probability that no one shares your birthday is given by;P(A)

= (365/365) * (364/365) * (363/365) *.... * ((365 - n + 1)/365)

= (365 * 364 * 363 * ... * (365 - n + 1))/(365)^n(b) Here, we are supposed to determine the least number of people we need to select so that the probability is at least 0.6 that at least one person shares our birthday. This is the of the probability that no one shares our birthday, i.e.,1 - P(A) ≥ 0.6 P(A) ≤ 0.4We know that, P(A)

= (365/365) * complement (364/365) * (363/365) *.... * ((365 - n + 1)/365)We can then use trial and error method or any numerical method to find the value of n such that P(A) ≤ 0.4We can use a spreadsheet, a calculator, or a software like R to carry out this calculation.Using R, we can run the following command to get the least value of n that satisfies the condition;> n

= 1while(prod((365 - (0:(n-1)))/365) > 0.4){n

= n + 1} > n [1] 24.The least number of people we need to select so that the probability is at least 0.6 that at least one person shares our birthday is 24 people.

To know more about probability visit:

https://brainly.com/question/31828911

#SPJ11

Answer:

y = 6x + 22

General Formulas and Concepts:

Pre-Alg

Algebra I

Slope Formula: \(m=\frac{y_2-y_1}{x_2-x_1}\)

Slope-Intercept Form: y = mx + b

Step-by-step explanation:

Step 1: Define

Point (-3, 14)

Point (-1, 16)

Step 2: Find slope m

Step 3: Find y-intercept b

Step 4: Write linear equation

y = 6x + 22

Answer:

8 dimes and 6 quarters

===================================================

Work Shown:

d = number of dimes

q = number of quarters

d+q = 14 since this is his coin total; equation solves to d = 14-q

10d+25q = 230 which is the total value in cents

10(14-q)+25q = 230 .... apply substitution rule

140-10q+25q = 230

15q+140 = 230

15q = 230-140

15q = 90

q = 90/15

q = 6 = number of quarters

d = 14-q

d = 14-6

d = 8 = number of dimes

-----------------

Check:

8 dimes + 6 quarters = 14 coins

8 dimes = 8*10 = 80 cents

6 quarters = 6*25 = 150 cents

8 dimes + 6 quarters = 80 cents + 150 cents = 230 cents = $2.30

The answers have been confirmed.

A CR less than or equal to 0.1 is considered acceptable, indicating a consistent set of judgments in comparing the criteria. If the CR is greater than 0.1, it is advised to revise the pairwise comparisons to improve consistency.

The Consistency Ratio (CR) in the context of the GEAR Matrix (which is related to bikes, not fruit) measures the level of consistency in judgments made when comparing criteria in a decision-making process, such as the Analytic Hierarchy Process (AHP). To calculate the CR for the Criteria in the GEAR Matrix, follow these steps:

1. Determine the pairwise comparison matrix by comparing the importance of each criterion against the others.
2. Calculate the weights of each criterion by normalizing the columns and finding the average for each row.
3. Multiply the pairwise comparison matrix by the weight vector to obtain a new vector.
4. Divide each element of the new vector by its corresponding weight to obtain the Consistency Vector.
5. Calculate the average of the Consistency Vector to get the Consistency Index (CI).
6. Divide the CI by the Random Index (RI) for the specific matrix size (this value can be found in AHP literature) to obtain the Consistency Ratio (CR).

A CR less than or equal to 0.1 is considered acceptable, indicating a consistent set of judgments in comparing the criteria. If the CR is greater than 0.1, it is advised to revise the pairwise comparisons to improve consistency.

to learn more about Matrix click here :

brainly.com/question/30389982

#SPJ11

a. U'(ct) = β(1 + r)U'(ct+1). This equation is known as the Euler equation, which represents the intertemporal marginal rate of substitution between consumption at time t and consumption at time t+1.

b. U'(c1) = β(1 + r)^2U'(c3). This relationship shows that the marginal utility of consumption at time 1 is equal to the discounted marginal utility of consumption at time 3.

c. C0 = ∑t=0[infinity]​(β(1 + r))^tct. This equation represents the sum of the discounted values of consumption at each period, where the discount factor β(1 + r) accounts for the diminishing value of future consumption.

d.  U0 = ∑t=0[infinity]​(β(1 + r))^tln(ct). This equation represents the sum of the discounted values of utility at each period, where the discount factor β(1 + r) reflects the time preference and the logarithmic utility function captures the agent's preference for consumption.

Y0 = y0 + (1 + γ)y1 + (1 + γ)^2y2 + ..., where γ represents the growth rate of income.

a. The optimization problem of the representative agent involves maximizing the present discounted value of utility subject to the period-by-period budget constraint. The Euler equation is derived as follows:

At each period t, the agent maximizes the utility function U(ct) = ln(ct) subject to the budget constraint ct = (1 + r)wt + yt, where wt is the agent's wealth at time t. Taking the derivative of U(ct) with respect to ct and applying the chain rule, we obtain: U'(ct) = β(1 + r)U'(ct+1). This equation is known as the Euler equation, which represents the intertemporal marginal rate of substitution between consumption at time t and consumption at time t+1.

b. The Euler equation between time 1 and time 3 can be written as U'(c1) = β(1 + r)U'(c2), where c1 and c2 represent consumption at time 1 and time 2, respectively.

Similarly, we can write the Euler equation between time 2 and time 3 as U'(c2) = β(1 + r)U'(c3). Combining these two equations, we fin

d U'(c1) = β(1 + r)^2U'(c3). This relationship shows that the marginal utility of consumption at time 1 is equal to the discounted marginal utility of consumption at time 3.

c. The present discounted value of optimal lifetime consumption can be written as C0 = ∑t=0[infinity]​(β(1 + r))^tct. This equation represents the sum of the discounted values of consumption at each period, where the discount factor β(1 + r) accounts for the diminishing value of future consumption.

d. The present discounted value of optimal lifetime utility can be written as U0 = ∑t=0[infinity]​(β(1 + r))^tln(ct).

This equation represents the sum of the discounted values of utility at each period, where the discount factor β(1 + r) reflects the time preference and the logarithmic utility function captures the agent's preference for consumption.

e. The present discounted value of lifetime income, denoted as Y0, can be expressed as Y0 = y0 + (1 + γ)y1 + (1 + γ)^2y2 + ..., where γ represents the growth rate of income. The income in each period is multiplied by (1 + γ) to account for the increasing income over time.

This assumption of income growth allows for a more realistic representation of the agent's economic environment, where income tends to increase over time due to factors such as productivity growth or wage increases.

for such more questions on  equation

https://brainly.com/question/17145398

#SPJ8

Answer:

yellow

Step-by-step explanation:

The intermediate value theorem states that if a continuous function takes on two values, a and b, at two points, c and d, respectively, then it must also take on every value between a and b at some point between c and d.

To use this theorem to show that the polynomial function f(x) = x⁵ + 2x⁴ + x³ + 3 has a real zero between -1.8 and -1.7, we need to evaluate f(-1.8) and f(-1.7) and show that they have opposite signs.

When x = -1.8, we have:

f(-1.8) = (-1.8)⁵ + 2(-1.8)⁴ + (-1.8)³ + 3
= -9.11552

When x = -1.7, we have:

f(-1.7) = (-1.7)⁵ + 2(-1.7)⁴ + (-1.7)³+ 3
= -4.85319

Since f(-1.8) is negative and f(-1.7) is positive, by the intermediate value theorem, f(x) must have a real zero between -1.8 and -1.7.  

To know more about polynomial visit :-

https://brainly.com/question/1496352

#SPJ11

The value that results when a number is multiplied by itself is known as the square root. So, to find the square root of 16, we need to find a number that, when multiplied by itself, equals 16. The value of the expression is 4.

One way to do this is to try different numbers and see if their square equals 16. For example, we can start with 1 and see if 1 times 1 equals 16. Clearly, 1 times 1 is 1, so we know that the square root of 16 is not 1.

Next, we can try 2. 2 times 2 is 4, which is less than 16, so we know that the square root of 16 must be greater than 2.

We can then try 3. 3 times 3 is 9, which is still less than 16, so the square root of 16 must be between 3 and 4.

Finally, we can try 4. 4 times 4 is 16, which means that the square root of 16 is indeed 4.

Therefore, the value of the given expression square root 16 is 4.

To learn more about square root follow the link:

https://brainly.com/question/1387049

#SPJ1

She needs to complete 20 laps for a total distance of 0.5 kilometer.

1 kilometers = 1000 meters

0.5 kilometers = 500 meters

Length of swimming pool = 25 meters

That means, she covers 25 meters in 1 lap.

Laps to cover 500 meters = 500/25

                                            = 20

Hence, she needs to do 20 laps.

To learn more about distance here:

https://brainly.com/question/15172156

#SPJ1

Answer:

Step-by-step explanation:

Here is the solutions though for 2,3:

For number 2:

180-90= 90 degrees for 2 angles.

90-10=80/2= 40 degrees for x

For number 3:

180-60=120

Then divide by 3=120/3=40 is x

Ps. It is weird both answer were 40 but I assure you that it is correct!