Compare the fatigue limits for polystyrene (Eioure 15.11) and the cast iron for which fatigue data are given in the table below: Stress Amplitude [MPa (ks)1 Cycles to Fallure 248 (36.0) 236 (34.2) 224 (32.5) 213 (30.9) 201 (29.1) 193 (28.0) 193 (28.0) 193 (28.0) 1 x 105 3 x 105 1 x 106 3 x 106 1 x 107 3 x 107 1 x 10 3 x 108 re the fatigue strengths at 10 cycles for poly(ethylene terephthalate) (PET, E oure 15.11) and 70Cu-302n (b) Compar brass (Eigure. B.21). polistyrene: MPa ductile cast iron: MPa poly(ethylene terephthalate (PET: MPa 70Cu-30Zn brass:

Answers

Answer 1

Firstly, let's focus on the given data for stress amplitude and cycles to failure for cast iron. We can see that as the stress amplitude decreases, the cycles to failure increase. This means that at lower stress amplitudes, cast iron has a higher fatigue limit and can withstand more cycles before failure.

Now, let's compare this to polystyrene. Unfortunately, there is no given data for polystyrene's fatigue limit in the question. However, we can make some general comparisons based on the properties of the materials. Polystyrene is a thermoplastic polymer, which means it is not as strong or durable as metals like cast iron. Therefore, we can assume that polystyrene's fatigue limit would be lower than cast iron's, meaning it can withstand fewer cycles before failure at a given stress amplitude.

Moving on to the comparison between PET and 70Cu-302n brass, we can again assume that the brass has a higher fatigue limit due to its metal properties. Brass is a copper-zinc alloy and is known for its strength and durability. PET, on the other hand, is a thermoplastic polymer similar to polystyrene and would have a lower fatigue limit.

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Related Questions

Please help me on this geometry please it needs to be done ASAP with work shown it says Find the area of the shaded region

Answers

area of the square = 16² = 256 cm²

area of the circle =

[tex]\pi {r}^{2} = 3.14 \times {8}^{2} = 200.96 \: {cm}^{2} [/tex]

therefore area of the shaded region is:

256 - 200.96 = 55 cm²

and the closest answer is D)

Answer:

D) 54.9 cm²

Step-by-step explanation:

The diagram shows a square with a circle inside it, and the question asks us to calculate the shaded area, which is the area inside the square not taken up by the circle.

The length of the sides of the square is 16 cm, and the radius of the circle can be seen to be half of that. Therefore, the radius of the circle is 8 cm.

To calculate the area of the shaded region, we have to first calculate the area of the square and then subtract the area of the circle inside.

• Let's calculate the area of the square first:

Area = side × side

        = 16 cm × 16 cm

        = 256 cm²

• Now let's calculate the area of the circle:

Area = π × r²

        = π × (8 cm)²

        = 64π cm²

• Finally, we have to simply subtract the area of the circle from the area of the square:

area of shaded region = 256 cm² -  64π cm²

                                     = 54.9 cm²

Therefore, the area of the shaded region is 54.9 cm², and the correct option is D.

those that 1100 is borrowed for seven years at an interest rate of 8% per year, compounded continuously. Find the amount owed assuming no payments are made until the end. do not round any intermediate computation and round your answer to the nearest cent 

Answers

$1,926.76 is the amount owed at the end of seven years, assuming no payments are made until the end.

To find the amount owed when $1100 is borrowed for seven years at an interest rate of 8% per year, compounded continuously, we can use the formula for continuous compound interest:

[tex]A = P * e^{(rt)[/tex]

In this case, P = $1100, r = 0.08, and t = 7. Plugging these values into the formula:

[tex]A = 1100 * e^{(0.08 * 7)[/tex]

Calculating the exponent:

[tex]A = 1100 * e^{(0.56)[/tex]

Using a calculator:

A = 1100 * 1.7516

A = $1,926.76

Therefore, the amount owed at the end of seven years, assuming no payments are made until the end, is approximately $1,926.76.

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In a scatter plot, if all data points were aligned along a 44º angle, the correlation would be_______. a) medium strength. b) low strength. c) high strength. d) 0

Answers

In a scatter plot, if all data points were aligned along a 44º angle, the correlation would be 0. The correct answer is D.

In a scatter plot, the correlation coefficient measures the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, where -1 indicates a perfect negative linear relationship, 1 indicates a perfect positive linear relationship, and 0 indicates no linear relationship.

When all data points are aligned along a 44º angle, it means that the points are distributed randomly and do not follow a clear linear pattern. There is no consistent increase or decrease in one variable as the other variable changes. Therefore, the correlation between the variables is 0, indicating no linear relationship or strength of association.

In other words, the angle of 44º suggests that the variables are unrelated and have no linear dependency on each other.

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Determine whether the subspaces are orthogonal: S_1 = span {[4 5 - 4], [0 1 1]}, S_2 = span {[5 -4 0]} S_1 = span {[1 1 1 1]}, S_2 = span {[-1 1 -1 1], [0 2 -2 0]} S_1 = span {[0 0 2 1], [0 0 1 -2]}, S_2 = span {[3 2 0 0], [0 1 -2 2]}

Answers

For subspaces to be orthogonal, their intersection must be the zero vector.

Therefore, we can determine whether the subspaces are orthogonal by checking if the dot product between any two vectors, one from each subspace, is equal to zero.
For S_1 and S_2, the dot product between [4 5 -4] and [5 -4 0] is not equal to zero, so they are not orthogonal.
For S_1 and S_2, the dot product between [1 1 1 1] and [-1 1 -1 1] and [0 2 -2 0] is equal to zero, so they are orthogonal.
For S_1 and S_2, the dot product between [0 0 2 1] and [3 2 0 0] and [0 1 -2 2] is equal to zero, so they are orthogonal.
Two subspaces are orthogonal if their vectors have a dot product of zero. For S_1 = span {[4 5 -4], [0 1 1]} and S_2 = span {[5 -4 0]}, the dot products are (4)(5) + (5)(-4) + (-4)(0) = 0. They are orthogonal.
For S_1 = span {[1 1 1 1]} and S_2 = span {[-1 1 -1 1], [0 2 -2 0]}, the dot product of S_1 and both vectors in S_2 is non-zero. They are not orthogonal.
For S_1 = span {[0 0 2 1], [0 0 1 -2]} and S_2 = span {[3 2 0 0], [0 1 -2 2]}, the dot product of all pairs of vectors is zero. They are orthogonal.

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the angle below measures 5.6 radians, and a circle is centered at the angle's vertex. the x -coordinate of the terminal point is 0.78. what is the y -coordinate of the terminal point?

Answers

The values will give you the y-coordinate of the terminal point.

To find the y-coordinate of the terminal point given the angle in radians (5.6) and the x-coordinate (0.78), we need to use the trigonometric functions.

First, we find the radius (r) of the circle using the cosine function:
cos(θ) = x-coordinate / r
cos(5.6) = 0.78 / r
r ≈ 0.78 / cos(5.6)

Now, we find the y-coordinate using the sine function:
sin(θ) = y-coordinate / r
sin(5.6) = y-coordinate / (0.78 / cos(5.6))

Finally, we can solve for the y-coordinate:
y-coordinate ≈ sin(5.6) * (0.78 / cos(5.6))

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evaluate (to true or false) the following expression: expression : (3 > 2 or 4 > 6) and (5 > 3)

Answers

The final evaluation of the expression is True.

The given expression is:

(3 > 2 or 4 > 6) and (5 > 3)

Let's evaluate it step by step:

(3 > 2) is true because 3 is greater than 2.

(4 > 6) is false because 4 is not greater than 6.

(5 > 3) is true because 5 is greater than 3.

Now, let's substitute the values into the expression:

(True or False) and True

The "or" operator evaluates to True if at least one of the conditions is true. In this case, the first condition is True, so the result of the "or" operation is True.

(True) and True

The "and" operator evaluates to True only if both conditions are true. In this case, both conditions are True, so the result of the "and" operation is True.

Therefore, the final evaluation of the expression is True.

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Mimi and Lindi each bought a dress in a sale. Mimi’s cost £65.45 and Lindi’s cost £52.65. Their mother had given them each two £50 notes and they were asked to give all the change back to their mother. What was the total amount of money their mother received?

Answers

In a case whereby Mimi and Lindi each bought a dress in a sale. Mimi’s cost £65.45 and Lindi’s cost £52.65 the total amount of money their mother received is £81.90.

How can the total amount of money their mother received be calculated?

Mimi’s dress cost = £65.45

Lindi’s dress cost  =£52.65

Amount received from the mother each = £100

Amount remained from Mimi after the dress = £100 -£65.45 =£34.55

Amount remained from Mimi after the dress = £100 -£52.65 =£47.35

total amount of money their mother received =£34.55 + £47.35=£81.90.

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what is the highest reality (the absolute), for hegel?

Answers

For Hegel, the highest reality or the absolute is referred to as the "Absolute Spirit" or the "Absolute Idea."

Hegel's philosophical system revolves around the concept of the dialectic, which involves the development and resolution of contradictions in a continuous process.

According to Hegel, the Absolute Spirit represents the ultimate truth or reality that encompasses and integrates all other forms of reality within it.

It is the highest stage of the dialectical process, where all contradictions are resolved and the full richness of reality is realized.

The Absolute Spirit is characterized by self-awareness, rationality, and the complete unity of subject and object. It is considered to be the ultimate source of all being and knowledge.

Hegel views reality as a dynamic and evolving process, and the Absolute Spirit is the culmination of this process.

It is important to note that Hegel's concept of the Absolute Spirit is highly abstract and philosophical in nature. It encompasses various aspects of human existence, including art, religion, philosophy, and history.

Hegel's philosophy aims to comprehend and articulate the nature of the Absolute through a systematic exploration of these different dimensions.

Overall, the Absolute, or Absolute Spirit, represents the highest reality and the ultimate goal of Hegel's philosophical system, encompassing the fullness of reality and reconciling the contradictions inherent in human experience.

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Toy rubber balls are packaged in a cylinder that holds 3 balls.
The diameter of each ball is 6.3 cm. Find the volume of the
cylinder. Use 3.14 for π

Answers

Answer:   V=  31.15665

Step-by-step explanation:

diameter divided by 2 to give 3.15 then multiply by 3.15

then squared

Answer:

392.58 cubic centimeters.

Step-by-step explanation:

The formula for the volume of a sphere is:

[tex]\boxed{\bold{V = \frac{4}{3}* \pi* r^3}}[/tex]

Given that the diameter of each ball is 6.3 cm, we can find the radius (r) by dividing the diameter by 2:

[tex]\bold{r = \frac{6.3 cm}{2} = 3.15 cm}[/tex]

Now we can calculate the volume of one ball:

[tex]V_{ball }= \frac{4}{3}* 3.14 * (3.15 cm)^3=130.86 cm^3[/tex]

We multiply the volume of one ball by 3 to find the total volume occupied by three balls,

[tex]V_{total} = 3 * V_{ball}[/tex]

Calculating the values:

[tex]V_{ball} = 3*130.86 cm^3=392.58 cm^3[/tex]

Therefore, the volume of the cylinder that holds the three rubber balls is approximately 392.58 cubic centimeters.

What is the Riemann Hypothesis?

Answers

the Riemann hypothesis is the conjecture that the Riemann zeta function

You would like to determine if the population probability of success differs from 0.70. You find 62 successes in 80 binomial trials. Implement the test at the 1% level of significance. (You may find it useful to reference the appropriate table: z table or t table)

a. Select the null and the alternative hypotheses.

H0: p = 0.70; HA: p ≠ 0.70

H0: p ≤ 0.70; HA: p > 0.70

H0: p ≥ 0.70; HA: p < 0.70

b. Calculate the sample proportion. (Round your answer to 3 decimal places.)

c. Calculate the value of test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)

d. Find the p-value.

p-value < 0.01

0.01 ≤ p-value < 0.025

0.025 ≤ p-value < 0.05

0.05 ≤ p-value < 0.10

p-value ≥ 0.10


e. At the 1% significance level, What is the conclusion?

Reject H0 since the p-value is smaller than significance level.

Reject H0 since the p-value is greater than significance level.

Do not reject H0 since the p-value is smaller than significance level.

Do not reject H0 since the p-value is greater than significance level.




f. Interpret the results at αα = 0.01.
We conclude that the population probability of success is greater than 0.70.

We cannot conclude that the population probability of success is greater than 0.70.

We conclude that the population probability of success differs from 0.70.

We cannot conclude that the population probability of success differs from 0.70.

Answers

The answers are:

(a) The null and alternative hypotheses are:

H₀: p = 0.70

[tex]H_A[/tex]: p ≠ 0.70

(b) Sample proportion = 62/80 ≈ 0.775

(c) The test statistic formula is:

Z = (p - p) / √(p(1-p) / n)

(d) the p-value is approximately 2 * (1 - 0.9573) ≈ 0.0854.

(e) Do not reject H₀ since the p-value (0.0854) is greater than the significance level of 0.01.

(f) At α = 0.01, we cannot conclude that the population probability of success differs from 0.70.

What is probability?

Probability is a branch of mathematics that deals with the study of random events or phenomena. It is the measure of the likelihood that an event will occur or not occur, expressed as a number between 0 and 1, where 0 represents impossibility and 1 represents certainty.

a. The null and alternative hypotheses are:

H0: p = 0.70 (population probability of success is 0.70)

HA: p ≠ 0.70 (population probability of success differs from 0.70)

b. To calculate the sample proportion, divide the number of successes (62) by the total number of trials (80):

Sample proportion = 62/80 ≈ 0.775

c. To calculate the test statistic, we can use the normal approximation to the binomial distribution. The test statistic formula is given by:

Z = (p - p) / √(p(1-p) / n)

Where:

p is the sample proportion

p is the assumed population proportion under the null hypothesis

n is the number of trials

Plugging in the values:

Z = (0.775 - 0.70) / √(0.70 * (1 - 0.70) / 80) ≈ 1.726

d. The p-value is the probability of obtaining a test statistic as extreme as the observed one, assuming the null hypothesis is true. We can find the p-value by looking up the absolute value of the test statistic (|Z| = |1.726|) in the standard normal distribution table.

The p-value is the probability in the tails of the distribution, so we need to find the sum of the probabilities in both tails. From the table, we find that the cumulative probability for Z = 1.72 is approximately 0.9573. Thus, the cumulative probability for Z = -1.72 is also approximately 0.9573.

Therefore, the p-value is approximately 2 * (1 - 0.9573) ≈ 0.0854.

e. At the 1% significance level, the conclusion is: Do not reject H0 since the p-value (0.0854) is greater than the significance level of 0.01.

f. At α = 0.01, we cannot conclude that the population probability of success differs from 0.70.

Hence, the answers are:

(a) The null and alternative hypotheses are:

H₀: p = 0.70

[tex]H_A[/tex]: p ≠ 0.70

(b) Sample proportion = 62/80 ≈ 0.775

(c) The test statistic formula is:

Z = (p - p) / √(p(1-p) / n)

(d) the p-value is approximately 2 * (1 - 0.9573) ≈ 0.0854.

(e) Do not reject H₀ since the p-value (0.0854) is greater than the significance level of 0.01.

(f) At α = 0.01, we cannot conclude that the population probability of success differs from 0.70.

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PLS HELP ASAP!!
1. Find the slope of the line through (2, -3) and (-4, 3).
-1
1
0
Find the slope of the line through (3, 4) and (0, 2).

3/2
2/3
-2/3

Answers

The slope of the line through (2, -3) and (-4, 3) is -1

The slope of the line through (3, 4) and (0, 2) is 2/3

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

The given two points are  (2, -3) and (-4, 3).

Plug in the values to find slope

slope = 3 + 3/-4-2

=6/-6

=-1

Now let us find slope of  line through (3, 4) and (0, 2).

m= 2-4/0-3

=-2/-3

=2/3

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The slope of the line passing through (2, -3) and (-4, 3) is -1.

The slope of the line passing through (3, 4) and (0, 2) is 2/3.

To find the slope of a line given two points, you can use the formula:

slope = (change in y-coordinates) / (change in x-coordinates)

Let's calculate the slope for each set of points:

(2, -3) and (-4, 3):

The change in y-coordinates is: 3 - (-3) = 6

The change in x-coordinates is: -4 - 2 = -6

slope = 6 / -6 = -1

Therefore, the slope of the line passing through (2, -3) and (-4, 3) is -1.

(3, 4) and (0, 2):

The change in y-coordinates is: 2 - 4 = -2

The change in x-coordinates is: 0 - 3 = -3

slope = -2 / -3 = 2/3

Therefore, the slope of the line passing through (3, 4) and (0, 2) is 2/3.

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How many men have a waist measurement of more than 85 cm

Answers

The number of men that has waist measurement of more that 85cm would be = 30 men.

How to calculate the number of men with waist measurement more than 85 cm?

To calculate the number of men whose waist measurement in more than 85cm, the content of the attached graph above is used.

The variables plotted in y-axis = cumulative frequency of total number of men.

The variables plotted in x-axis = waist measurement in cm

Number of men with waist measurement 85cm = 10

Number of men with waist measurement 115cm = 40

Therefore, the waist measurement of men more than 85cm = 40-10 = 30 men.

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Use the cofunction identities Question Write the following function in terms of its cofunction.

csc(13)
When writing your answer, do not include the degree symbol, and make sure to use parentheses. For example, if the answer were cos(23), you would enter cos(23).
Provide your answer below:

Answers

csc(13) is equivalent to sec(90-13), using the cofunction identity for sine and cosine. Therefore, the function in terms of its cofunction is sec(77).

A cofunction is a mathematical relationship between trigonometric functions that involves the complementary angles of a right triangle.

In a right triangle, the two acute angles are complementary, meaning their sum is 90 degrees (π/2 radians). The cofunctions of two angles are related by the following identities:

sin(θ) = cos(π/2 - θ)

cos(θ) = sin(π/2 - θ)

tan(θ) = cot(π/2 - θ)

cot(θ) = tan(π/2 - θ)

sec(θ) = csc(π/2 - θ)

csc(θ) = sec(π/2 - θ)

These identities indicate that the value of one trigonometric function of an angle is equal to the cofunction of the complementary angle.

For example, if θ is an angle, then sin(θ) is equal to cos(π/2 - θ). Similarly, cos(θ) is equal to sin(π/2 - θ). These identities allow us to express a trigonometric function in terms of its cofunction, which can be useful in certain calculations and simplifications.

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in problems 1–10, determine all the singular points of the given differential equation. 1. 1x 12y″ - x2 y′ 3y = 0

Answers

The singular points of the given differential equation are x = 0.

To determine the singular points of the given differential equation, we need to find the values of x at which the coefficients of y", y', and y become zero or undefined.

For the given differential equation: x^12y″ - x^2y' + 3y = 0

Singular points due to coefficient of y":

The coefficient of y" is x^12. It becomes zero at x = 0.

Singular points due to coefficient of y':

The coefficient of y' is -x^2. It becomes zero at x = 0.

Singular points due to coefficient of y:

There is no explicit coefficient of y in the given equation, so there are no singular points due to the coefficient of y.

Therefore, the singular points of the given differential equation are x = 0.

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Let X1, ..., Xn be a random sample from a Nu, 1) population. Find the MLE of μ.

Multiple Choice

a.1/x
b. - 1x
c. X
d. X-1

Answers

If  X1, ..., Xn be a random sample from a Nu, 1) population then the MLE of μ is X, option C is correct.

We have a random sample X1, ..., Xn from a population with an unknown mean μ.

The goal is to find the Maximum Likelihood Estimator (MLE) of μ.

The MLE approach seeks to find the parameter value that maximizes the likelihood function, which measures the probability of observing the given sample data.

The likelihood function is based on the distribution assumption of the population, which is specified as "Nu, 1."

The Maximum Likelihood Estimator (MLE) of μ, the population mean, can be found by taking the sample mean of the random sample X1, ..., Xn.

Hence, the MLE of μ is simply the sample mean, which is represented by X

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Find the cross products u * v and v * u for the vectors u = <3,4,-7> and v = <-1,1,-1>

Answers

The cross products are:
u × v = <3, -4, 7>
v × u = <-11, 22, -13>

To find the cross products u × v and v × u for the vectors u = <3, 4, -7> and v = <-1, 1, -1>, we will use the cross product formula:
u × v = <(u₂v₃ - u₃v₂), -(u₁v₃ - u₃v₁), (u₁v₂ - u₂v₁)>
For u × v:
u × v = <(4 * -1 - (-7) * 1), -((3 * -1 - (-7) * -1)), (3 * 1 - 4 * -1)>
u × v = <(-4 + 7), -(-3 + 7), (3 + 4)>
u × v = <3, -4, 7>
For v × u, just swap u and v in the formula:
v × u = <(-7 - 4), -((-1 - 21)), (-1 - 12)>
v × u = <-11, 22, -13>
So, the cross products are:
u × v = <3, -4, 7>
v × u = <-11, 22, -13>

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For the regression equation, y = -2X + 6, if the X value is above the mean (positive deviation), then what can be determined about the predicted Y value?
a. The predicted Y value will be above the mean for the Y scores
b. The predicted Y value will be below the mean for the Y scores.
c. It is impossible to determine where the predicted Y value will be.

Answers

The correct answer to the question is (b) The predicted Y value will be below the mean for the Y scores. The coefficient -2 represents the slope of the line, which means that for every increase of 1 unit in X, Y will decrease by 2 units. The intercept 6 represents the point where the line intersects the Y-axis.


The equation y = -2X + 6 is a linear equation that describes the relationship between X and Y.Now, if the X value is above the mean (positive deviation), that means it is further to the right of the X-axis than the mean. This also means that the predicted Y value will be lower than the mean for the Y scores. This can be seen by plugging in a value that is above the mean into the equation, which will result in a negative value for Y. Therefore, the correct answer to the question is (b) The predicted Y value will be below the mean for the Y scores.
In summary, knowing the regression equation and the deviation of the X value from the mean allows us to predict the direction and degree of change in the Y value.

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a wireless carrier offers the following plans that a person is considering. the family plan: $100 monthly fee, unlimited talk and text on up to 5 lines, and data charges of $35 for each device for up to 2 gb of data per device. the mobile share plan: $140 monthly fee for up to 10 devices, unlimited talk and text for all the lines, and data charges of $15 for each device up to a shared total of 10 gb of data. find the model of the total cost of the family plan in dollars. use p for the number of devices that need data plans as part of their cost.

Answers

The model of the total cost of the family plan in dollars for p devices is given by, C(p) = 100 + 35 p, where C(p) is the total cost.

Family plan offers $ 100 fixed monthly fee and unlimited talk and text on up to 5 lines and data charges of $ 35 for each device for up to 2 gb of data per device.

Mobile share plan offers $140 monthly fee for up to 10 devices, unlimited talk and text for all the lines, and data charges of $15 for each device up to a shared total of 10 gb of data.

Here number of devices which need data plans as part of their cost is ' p '.

So the model which depicts the total cost of family plan is given by,

C(p) = 100 + 35 p, where C(p) is the total cost.

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HELP asap major grade i need answers!!

Answers

Answer of the statements is describe below.

Given that,

For general :

cost of admission  = $15

cost of per taco = $4

For VIP :

cost of admission  = $36

cost of per taco = $1.50

Therefore,

Since price of taco in VIP is less than General admission

Then Deric should choose VIP if he plan to buy 6 tacos.

The amount Deric have to spent = $55

As Deric wants to eat many tacos so he should go for VIP in which price of taco in VIP is less than General admission so he can buy more taco.

Since price of each taco in general admission = $4

Then he can buy 55/4  = 13.74 tacos in general admission

And  price of each taco in VIP = $1.5

Then he can buy 55/1.5 = 36.66 tacos in VIP

Since price of tacos in VIP is cheaper then he can buy

37 tacos nearly.

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in a random sample of size n = 77, find pry >78. pry >78 = enter your response here

Answers

To find pry >78 in a random sample of size n = 77, we would need more information such as the mean and standard deviation of the sample.

Based on the given information, we need to find the probability that a random variable Y is greater than 78 (pr(Y > 78)) in a sample of size           n = 77.

To provide a precise answer, additional details about the distribution of the data (mean and standard deviation) are needed. However, once you have these values, you can use the Z-score formula to calculate the probability.

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andy is making square signs of different sizes. the supplies are limited. andy restricts the area of each sign to 100 square inches or less using the inequality 0 < s^2 ≤ 100.

complete the inequality to show the range of the possible side lengths, s, in inches

Answers

The range of possible side lengths, s, in inches for the square signs is: 0 < s ≤ 10

How to complete the inequality to show the range of the possible side lengths

To show the range of possible side lengths, s, in inches for the square signs with an area of 100 square inches or less, we can complete the inequality based on the given restriction: 0 < s^2 ≤ 100

To isolate s, we can take the square root of both sides of the inequality:

[tex]\sqrt{(0)} < \sqrt{(s^2)} \leq \sqrt{100}[/tex]

0 < s ≤ 10

Therefore, the range of possible side lengths, s, in inches for the square signs is: 0 < s ≤ 10

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if the insured cancels a fire insurance policy after seven months, the refund will be less than if the insured cancels the policy.
O TRUE
O FALSE

Answers

False. The statement is not necessarily true. The refund amount for canceling a fire insurance policy after seven months can vary depending on the specific terms and conditions outlined in the insurance policy.

Generally, insurance policies contain provisions regarding cancellations and refunds. Some policies may offer a pro-rata refund, which means the insured will receive a refund proportionate to the unused portion of the policy period. In such cases, canceling the policy after seven months would result in a higher refund compared to canceling it earlier. However, it is important to review the terms of the specific insurance policy to determine the exact refund amount. Other factors such as administrative fees or penalties for early cancellation may also affect the refund amount.

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the area of a 6 metre wide road outside a garden in all its four sides is 564 sq. m. if the length of the garden is 20 m. what is its breadth?

Answers

The breadth of the garden is 17.625 meters.

To find the breadth of the garden, we can subtract the area of the road surrounding the garden from the total area of the rectangle formed by the length and breadth of the garden.

Given that the width of the road is 6 meters and the total area of the road is 564 square meters, we can calculate the area of the garden by subtracting the road area from the total area.

Total area = Length * Breadth

564 = (20 + 2 * 6) * Breadth

564 = 20 * Breadth + 12 * Breadth

564 = 32 * Breadth

Now, divide both sides of the equation by 32 to isolate the breadth:

Breadth = 564 / 32

Breadth ≈ 17.625 meters

Therefore, the breadth of the garden is approximately 17.625 meters.

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what is the probability of coming up with the correct unscrambling through random letter selection?

Answers

the probability of randomly selecting the correct unscrambling would be 1/n!. As the length of the word increases, the probability of randomly selecting the correct unscrambling becomes increasingly small due to the exponential growth of possible arrangements.

The probability of coming up with the correct unscrambling through random letter selection depends on the specific word being unscrambled and the number of possible permutations. In general, the probability can be quite low due to the large number of possible combinations.

To calculate the probability, you would need to know the total number of possible letter arrangements and the number of arrangements that result in the correct unscrambling. Let's assume we have a word with n letters. The total number of possible arrangements is n!, which represents n factorial (the product of all positive integers from 1 to n).

The number of arrangements that result in the correct unscrambling depends on the specific word and the length of the word. For example, if the word has 4 letters, there are 24 possible arrangements (4!). However, only one of those arrangements is the correct unscrambling.

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In order to test the following hypothesis (The Null: mu1 - mu 2 is less than or equal to 0. The Alternative: mu1 - mu 2 is greater than 0) at an alpha level of significance and sigma is known, the null hypothesis will be rejected if Z isa. < = z alphab. > = z alphac. < = (-)z alphad. < 0

Answers

In order to test the given hypothesis, we need to compare the test statistic (Z) with the critical value (Z alpha), where alpha is the level of significance. Since the alternative hypothesis states that mu1 - mu2 is greater than 0, we are interested in the right-tailed test.

This means that we need to find the critical value for the upper tail area under the standard normal distribution, which corresponds to the level of significance.

The null hypothesis will be rejected if the test statistic (Z) is greater than the critical value (Z alpha). Therefore, the correct option is (b) > = z alpha. This means that if the calculated value of Z is greater than or equal to the critical value of Z alpha, we can reject the null hypothesis in favor of the alternative hypothesis at the given level of significance.

It's important to note that the value of sigma is known in this case, which means that we can use the standard normal distribution to calculate the critical value and the test statistic. In summary, we reject the null hypothesis if Z is greater than or equal to the critical value Z alpha, which corresponds to the level of significance alpha for a right-tailed test.

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Find the quotient and remainder for

Answers

The quotient is (x + 3) while the remainder is (12x - 3)

What is the quotient and remainder?

[tex] \frac{ {2x}^{3} - {8x}^{2} + 7x - 12 }{ {2x}^{2} + 5 } [/tex]

The dividend is 2x³ - 8x² + 7x - 12

The divisor is 2x² + 5

Quotient is the results of dividing a divided by a divisor.

x + 3\\ \sqrt[ {2x}^{2} + 5]{ {2x}^{3} - {8x}^{2} + 7x - 12 } \\ {2x}^{2 } + 5x \\ {6x}^{2} + 12x \ \\ {6x}^{2} + 15 \\ 12x - 3

Hence, (x + 3) and (12x - 3) are the quotient and remainder respectively.

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use the remainder term to estimate the absolute error in approximating the following quantity with the nth-order taylor polynomial centered at 0. tan0.25, n=2 Select the choice below and fill in the answer box to complete your choice. Use scientific notation. Use the multiplication symbol in the math palette as needed. Do not round until the final answer. Then round to two decimal places as needed.

Answers

To estimate the absolute error in approximating tan(0.25) using the 2nd-order Taylor polynomial centered at 0, we need the remainder term expression.

What is the remainder term expression for the given approximation?

In Taylor series approximation, the remainder term represents the difference between the actual value of a function and its approximation using a truncated Taylor polynomial. It helps estimate the absolute error of the approximation.

The remainder term for the 2nd-order Taylor polynomial centered at 0 is given by the formula: Rn(x) = f'''(c) * (x - a)^n / (n+1)!, where f'''(c) represents the third derivative of the function at some point c between 0 and 0.25.

To estimate the absolute error in approximating tan(0.25) using the 2nd-order Taylor polynomial, we need the value of the third derivative of the tangent function and the point c between 0 and 0.25 at which we evaluate it. Without this information, we cannot calculate the exact value of the remaining term or the absolute error.

To obtain an estimate of the absolute error, we would need to evaluate the remainder term at a specific value of c and substitute it into the expression. Without the given value of c or the third derivative of the tangent function, we cannot provide a numerical estimation of the absolute error in this case.

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PLS IM DESPERATE Which input/output table corresponds to the graph of the function shown below?

Answers

The coordinate of the points will be (0, 1), (2, 2), (4, 3), and (6, 4). Thus, the correct option is C.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

From the graph, the value of the y-intercept is 1. And the slope is 1/2. Then the equation is given as,

y = (1/2)x + 1

From the graph, the coordinate of the points will be (0, 1), (2, 2), (4, 3), and (6, 4).

Thus, the correct option is C.

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the principal would like to assemble a committee of 15 students from the 20-member student council. how many different committees can be chosen?

Answers

There are 15,504 different committees that can be chosen from the 20-member student council to form a committee of 15 students.

To calculate the number of different committees that can be chosen from a 20-member student council to form a committee of 15 students, we can use the combination formula.

The number of combinations of selecting 'r' items from a set of 'n' items is given by the formula:

C(n, r) = n! / (r!(n - r)!)

In this case, we want to select 15 students from a pool of 20 members, so the formula becomes:

C(20, 15) = 20! / (15!(20 - 15)!)

Calculating this value:

C(20, 15) = 20! / (15! * 5!)

The factorial notation represents the product of all positive integers up to a given number. Evaluating the factorials:

20! = 20 * 19 * 18 * 17 * 16 * 15!

15! = 15 * 14 * 13 * 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5!

By canceling out common factors:

C(20, 15) = (20 * 19 * 18 * 17 * 16) / (5 * 4 * 3 * 2 * 1)

Simplifying:

C(20, 15) = 15,504

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