Pls answer you’ll get 100 points

Pls Answer Youll Get 100 Points

Answers

Answer 1

Take 2points

(0,0)(3,2)

Equation in two point form

\(\\ \sf\longmapsto y-y_1=\left(\dfrac{y_2-y_1}{x_2-x_1}\right)x-x_1\)

\(\\ \sf\longmapsto y-0=\dfrac{2-0}{3-0}(x-0)\)

\(\\ \sf\longmapsto y=\dfrac{2}{3}x\)

.

Option D is correct

Answer 2

the upper one ans is write


Related Questions

Paula says that 2/3 is equivalent to 4/9 because 4 is a multiple of 2 and 9 is a multiple of 3. explain her error.

Answers

Answer:

Paula is wrong because, in order to be equivalent, the nominator and denominator of a fraction must have to be multiplied by the same number.

Step-by-step explanation:

Paula is wrong because, in order to be equivalent, the nominator and denominator of a fraction must have to be multiplied by the same number.

4/9 is basically obtained when we multiply the denominator of 2/3 by 2 and denominator by 3, which is wrong.

Thus, the correction is as follows:

Given the fraction

\(\frac{2}{3}\)

Multiply the nominator and denominator of the fraction by 2

\(\frac{2\times 2}{3\times 2}=\frac{4}{6}\)

Thus, the 4/6 is the correct equivalent expression of 2/3.

BRAINLIEST For the fastest answer
Hello I need help on this math question

ignore My circled answer it MIGHT be wrong if it's not let me know :)​

BRAINLIEST For the fastest answerHello I need help on this math questionignore My circled answer it MIGHT

Answers

Answer:

the answer is b wait I can also be c and d

Answer:

A. 37°

Step-by-step explanation:

BRAINLIEST For the fastest answerHello I need help on this math questionignore My circled answer it MIGHT

Compute the following quantities to the correct number of significant figures. (a) 5.0000×2 (b) 5.0000×2.0 (c) 2.5×10
−2
−2.5 (d)
2.5×10
−2
−2.500

(e) 5.0000÷2 (f) 2.5×10
−2
−π

Answers

(a) 5.0000 × 2 = 10.000, which should be rounded to 10 (one significant figure).

(b) 5.0000 × 2.0 = 10.000, which should be rounded to 10 (two significant figures).

(c) 2.5 × 10^(-2) = 0.025, which has two significant figures.

(d) 2.5 × 10^(-2) - 2.500 = -0.000, which should be rounded to 0 (one significant figure).

(e) 5.0000 ÷ 2 = 2.5000, which should be rounded to 2.5 (three significant figures).

(f) 2.5 × 10^(-2) - π = -0.0314159265, which should be rounded to -0.031 (three significant figures).

In each case, the final answer is rounded to the correct number of significant figures based on the least precise number in the calculation. The significant figures represent the meaningful and reliable digits in a number, and they indicate the precision of the measurement or calculation. When performing arithmetic operations, it is important to consider the significant figures and round the result accordingly to maintain accuracy and avoid misleading values.

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Taylor currently earn $24. 00 an hour at her job. Thank to her hard work, her bo i going to give her a 15% raie. How much will he earn each hour after the raie?

Answers

Answer:

Taylor will earn $27.60 after the raise.

Step-by-step explanation:

If you take $24.00 and multiply it by $1.15, your answer should be $27.60. Therefore, this is the answer to your question.

Hopefully this helps, did the best I could!

please help will mark brainlist​

please help will mark brainlist

Answers

Step-by-step explanation:

Step by Step Solution:

More Icon

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "/-19" was replaced by "/(-19)".

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

s/(-19)-(-29)=0

Step by step solution :

STEP

1

:

s

Simplify ———

-19

Equation at the end of step

1

:

s

——— - -29 = 0

-19

STEP

2

:

Rewriting the whole as an Equivalent Fraction

2.1 Subtracting a whole from a fraction

Rewrite the whole as a fraction using -19 as the denominator :

-29 -29 • -19

-29 = ——— = —————————

1 -19

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

2.2 Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

s • -1 - (-29 • 19) 551 - s

——————————————————— = ———————

19 19

Equation at the end of step

2

:

551 - s

——————— = 0

19

STEP

3

:

When a fraction equals zero

3.1 When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

551-s

————— • 19 = 0 • 19

19

Now, on the left hand side, the 19 cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

551-s = 0

Solving a Single Variable Equation:

3.2 Solve : -s+551 = 0

Subtract 551 from both sides of the equation :

-s = -551

Multiply both sides of the equation by (-1) : s = 551

Kevin has 17 trading cards. Billy has more trading cards than Kevin. Choose the expression that shows how many trading cards Billy has.
A. t
B. t+17
C.17-t
D.t-17

Answers

Answer:

t + 17

Step-by-step explanation:

it’s this because, t + 17 = more than what Kevin has t = 17 I’m assuming which is why it’s B. Or t + 17.

What number is furthest from 0 on a number line? 16 or 18?

Answers

18. _______________________________________

what is slope if -3

Answers

Answer:

yep

Step-by-step explanation:

it’s a negative slope so it would go up 3 and left 1

Find the length of the third side?

Find the length of the third side?

Answers

Answer:

\(3\sqrt{5}\)

Step-by-step explanation:

Let’s say the third length is x. We can use the Pythagorean Theorem which states that a^2 + b^2 = c^2 where a and b are the legs and c the hypotenuse. Using Pythagorean Theorem, we can see that x^2 + 6^2 = 9^2. Solving we get that x^2 = 45 -> x = \(3\sqrt{5}\)

I hope this helps!!! :)

What is the addition and subtraction rule with significant figures? Please give some specific examples.

Answers

When adding or subtracting numbers with significant figures, the result should be rounded to the least precise decimal place of the measurements involved.

How do you round the result when adding or subtracting significant figures?

When performing addition or subtraction operations with numbers that have different levels of precision, it is important to ensure that the result is reported with the appropriate number of significant figures.

The rule states that the result should be rounded to the least precise decimal place among the measurements involved in the calculation.

For example, consider the addition of 53.5 and 46.5. Both numbers have one decimal place, so the sum should also be reported with one decimal place.

Adding the numbers gives us 100, but when applying the rule, we round the result to 100.0 to reflect the precision of the original measurements.

Similarly, if we subtracted 46.5 from 53.5, the result would still have one decimal place: 7.0.

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Point R is at (3, 1.3) and Point T is at (3, 2.4) on a coordinate grid. The distance between the two points is
. (Input numbers and decimal point only, such as 8.2.) (3 points

Answers

Answer:

1.05

Step-by-step explanation:

√((3 -3) + (2.4 - 1.3))

√(0 + 1.1)

√1.1 ≈ 1.05

Given the equation startfraction 2 x 2 over y endfraction = 4 w 2 what is the value of x? x = y w y minus 1 x = 2 y w y minus 1 x = 2 y w y minus 2 x = 4 y w 2 y minus 2

Answers

The value of x is 2yw + y - 1 for the given equation 2x + 2/y = 4w + 2.

According to the given question.

We have an equation

2x + 2/y = 4w + 2

Since, we have to find the value of x for the given equation

2x + 2/y = 4w + 2

Thereofore,

2x + 2/y = 4w + 2

⇒ 2(x + 1)/y = 2(2w + 1)    (taking 2 common from both the sides)

⇒ (x + 1)/y = 2w + 1

⇒ (x + 1) = y(2w + 1)         (multiplying both the sides by y)

⇒ x + 1 = 2yw + y

⇒ x = 2yw + y - 1         ( subtracting 1 both the sides)

Hence, the value of x is 2yw + y - 1 for the given equation 2x + 2/y = 4w + 2.

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Which number-line model represents the sum of 3/4 + ( - 1.75) ?​

Which number-line model represents the sum of 3/4 + ( - 1.75) ?

Answers

Answer:

A

Step-by-step explanation:

Michael is saving to buy his senior ring. The base cost of the ring is $280. There are also upgrades he can purchase for the ring. If he saves $35 each month, Which solution represents how many months it will take Micheal before he can purchase his ring?

A.x<_8
B.x_>8
C.x<8
D.x>8​

Answers

Answer:

B

Step-by-step explanation:

Assuming that he doesn't buy any upgrades it will take 280/35 = 8 months to save enough money to buy the ring. Taking the possibility that he may buy an upgrade too we can say that it will take 8 months or more to buy the ring.

PLEASE ANSWER THIS QUICK AND RIGHT!! 50 POINTS
DETERMINE THE PERIOD

PLEASE ANSWER THIS QUICK AND RIGHT!! 50 POINTSDETERMINE THE PERIOD

Answers

The period of the given trigonometric function is: 20.

What is the period of the trigonometric graph?

The distance between the repetition of any function is called the period of the function. For a trigonometric function, the length of one complete cycle is called a period.

Sine and cosine functions start repeating the same pattern of y-axis values after every 2(pi). The period is defined as just the distance on the x-axis before the pattern repeats.

Now, looking at the trigonometric graph, we see that the x-interval for which the graph repeats itself is 20

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i need the answer for this 2120 = 18x + 320

Answers

Answer:

100

Step-by-step explanation:

we need to swap sides so we take the 320 and put it in the other side but in negative form and that comes out to 1800 and then we divide that by 18

Answer:

x = 100

Step-by-step explanation:

2120 - 320 = 1800

1800 ÷ 18 = 100

for each of the following determine the n -unit percent change. the 19-unit percent change is 45 %. what is the 17-unit percent change? % the 16-unit percent change is 43 %. what is the 12-unit percent change? % the 20-unit percent change is -25 %. what is the 18-unit percent change? % the 5-unit percent change is -50 %. what is the 8-unit percent change?

Answers

Hence, 17-unit percent change is (45/19)×17% = 40.26%

12-unit percent change is (43/16)×12% = 32.25%

18-unit percent change is (-25/20)×18% = -22.5%

8-unit percent change is (-50/5)×8% = -80%

Given, that

The 19-unit percent change is 45 %

Now, 1-unit percent change is 45/19

17-unit percent change is (45/19)×17%

= 40.26%

The 16-unit percent change is 43 %

Now, 1-unit percent change is 43/16

12-unit percent change is (43/16)×12%

= 32.25%

The 20-unit percent change is -25%

Now, 1-unit percent change is -25/20

18-unit percent change is (-25/20)×18%

= -22.5%

The 5-unit percent change is -50 %

Now, 1-unit percent change is -50/5

8-unit percent change is (-50/5)×8%

= -80%

Hence, 17-unit percent change is (45/19)×17% = 40.26%

12-unit percent change is (43/16)×12% = 32.25%

18-unit percent change is (-25/20)×18% = -22.5%

8-unit percent change is (-50/5)×8% = -80%

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Define P(n) to be the assertion that:
n(n1)(2n 1)πΣε6j=1
(a)Verify that P(3) is true.
(b)Express P(k).
(c)Express P(k + 1).
(d)In an inductive proof that for every positive integer n,
=n(n+1)(2n 1)6j=1
what must be proven in the base case?
(e)In an inductive proof that for every positive integer n,п(п + 1)(2n + 1)6j=1
what must be proven in the inductive step?
(f)What would be the inductive hypothesis in the inductive step from your previous answer?
(g) Prove by induction that for any positive integer n,
п(п + 1)(2n + 1)j=1

Answers

The assertion that which shows that P(k + 1) is true provided Pk in the Inductive step is true. Moreover, P(1) is also true. Hence, by induction principle, we can say that P(n) is true for all positive integer n.

What is Integer?

A zero, a positive natural number, or a negative integer with a minus sign is an integer. The negative numbers are the additive inverses of their positive counterparts.

Given that P(n) be the assertion

∑j² = n (n+1)(2n+1)/6

(a) For n = 3, we get

∑j² = 1² + 2²+3² =14

= 3(3+1)(6+1)/6

=14

Hence, P(3) is true.

(b) Expression for P(k) may take the form

∑j² = k (k+1)(2k+1)/6

(c) Expression for P(k + 1) may take the form

∑j² = (k+1) (k+2)(2k+3)/6

(d)Base case:

In base case, we must prove that P(1) is true.

(e) To prove P(n) will be true for every positive integer n, we need to prove that P(k + 1) is true in the inductive step, where k is a positive integer.

(f) In the Inductive step, the Inductive hypothesis is that Pk is true for positive integer k.

(g)Base case:

a) For n=1, we get

RHS= 1(1+1)(2+1)/6

=1

Hence, P(1) is true.

Inductive hypothesis:

Assume P(k) is true:

∑j² = k (k+1)(2k+1)/6

Inductive step:

Now,

∑j² = k (k+1)(2k+1)/6 +(K+1)²

which shows that P(k + 1) is true provided P(k) in the Inductive step is true. Moreover, P(1) is also true. Hence, by induction principle, we can say that P(n) is true for all positive integer n.

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a large group of people is to be checked for two common symptoms of a certain disease. it is thought that 20% of the people possess symptom a alone, 40% possess symptom b alone, 10% possess both symptoms, and the remainder have neither symptom. for one person chosen at random from this group, find the following probabilities. (a) the person has neither of the symptoms. (b) the person has at least one symptom. (c) the person has both symptoms, given that he has symptom b. (round your answer to two decimal places.)

Answers

(A) A person's chance of experiencing neither symptom is 30%. (b) Seventy percent of people are likely to experience at least one symptom. (c) If a person has symptom B, there is a 25% chance that they will also have both symptoms.

(A) The individual exhibits neither symptom:

Let's write P(A) for the likelihood of having symptom A and P(B) for the likelihood of having symptom B. Given that 20% of people only have symptom A, 40% only have symptom B, and 10% only have both symptoms, the likelihood of having neither symptom can be determined as follows:

100% - P(A) - P(B) - P(both symptoms) - P(neither symptom)

P(none of the symptoms) = 100% – 20% – 40% – 10% = 30%

As a result, there is a 30% chance that a randomly selected person will exhibit neither symptom.

(b) At least one symptom is present in the person.

We can use the complement rule to calculate the likelihood that at least one symptom will be present. Neither symptom is the opposite of having at least one symptom. Because of this, P(at least one symptom) = 1 - P(neither symptom), and P(at least one symptom) = 1 - 0.30 = 0.70.

Therefore, there is a 70% chance that a randomly selected individual has at least one symptom.

(c) The person has both symptoms, given that they have symptom B:

To calculate this conditional probability, we use the formula:

P(both symptoms | symptom B) is equal to the product of P(both symptoms and symptom B) / P(symptom B).

We are informed that 40% of people only have symptom B whereas 10% have both symptoms. P(both symptoms | symptom B) = (10% / 40%) = 0.25 as a result.

Given that they have symptom B, a randomly selected person has a 25% chance of having both symptoms.

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Which of the following is the function rule for the graph of the sin function from 0 to 2pi if the amplitude is 1.5 and the period is (pi/2)?
A. 1.5sin(pi /4)x
B. 1.5sin2x
C. 1.5sin4x

please help fast, will give brainliest

Answers

Answer:

1.5sin4x

Step-by-step explanation:

I just answered this question and got it right.

The function is 1.5sin(4x).

What is sin function?

The ratio of the length of the opposite side to that of the hypotenuse in a right-angled triangle is the sine function in trigonometry. A right triangle's sides or unknown angles can be found using the sine function.

Given the sine function from (0, 2π), and amplitude is 1.5, the period is π/2

sine function in general form

y = a sin (b (x – h)) + d

where a = amplitude, b= period

h is the phase shift, and

d is the vertical displacement.

according to question, This function currently has no phase shift, since

h = 0, and  no vertical displacement, since d = 0

equation is  y = a sin b x

and b is ratio of normal period to desired period

b = 2π/(π/2)

b = 4

substitute the value of a and b in equation we get,

y = 1.5 sin (4x)

Hence the sin function from 0 to 2pi is y = 1.5 sin (4x).

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The ratio of the measures of the sides of a triangle is 9:12:5. If the perimeter of the triangle is 130 feet, find the measure of the sides.

Answers

Answer:

The sides of the triangle are 45, 60, and 25 ft

Step-by-step explanation:

9 + 12 + 5 equals 26.

Now we need to get the first two sides.

9/26 × 130 = 1170/26 = 45

In order to obtain the other side;

12/26 = 1560/26 = 60

And to obtain the third side:

5/26 × 130 =650/26 = 25

Therefore, the sides of the triangle are 45, 60, and 25 ft

I hope this helps! ^-^

What are the properties of Laplace transform table?

Answers

The Laplace transform table contains properties and formulas for common transforms, as well as the inverse Laplace transform and the shift theorem. It also includes properties such as linearity, scaling, and time shifting.

The Laplace transform table is an important tool for solving linear differential equations. It contains information about common transformations and their associated formulas, as well as the inverse Laplace transform and the shift theorem. The table also includes properties such as linearity, scaling, and time shifting. Linearity states that if a function f(t) is a linear combination of two functions f1(t) and f2(t), then its Laplace transform F(s) is the sum of the Laplace transforms of f1(t) and f2(t). Scaling states that if a function f(t) is multiplied by constant k, then its Laplace transform F(s) is divided by k. Time shifting states that if a function f(t) is shifted by x units in time, then its Laplace transform F(s) is multiplied by \(e^(-sx)\). These properties can be used to simplify Laplace transforms and to solve linear differential equations. The Laplace transform table is a useful tool for engineers and physicists who use linear differential equations in their work.

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Fruchter Corporation keeps careful track of the time required to fill orders. The times, recorded for a particular order are shown. What was the throughput time?

Answers

Answer:

11.0 hours

Step-by-step explanation:

The times, recorded for a particular order are shown below:

Move time                     2.7 hours

Wait time                       26.4 hours

Queue time                   6.4 hours

Process time                  1.8 hours

Inspection time              0.1 hours

Throughput time is also known as cycle time/ manufacturing throughput time, it is the time needed to produce an item. It is the time taken for the item/product to be converted from a raw material into a product ready for use. The throughput time is the sum of the move time, queue time, process time and inspection time.

Throughput time = move time + queue time + process time + inspection time.

Throughput time = 2.7 hrs + 6.4 hrs + 1.8 hrs + 0.1 hrs = 11 hrs

Change the word phrase to an algebraic expression. Use x to represent the number. The product of 9 and two more than a number

Answers

The algebraic expression for "The product of 9 and two more than a number" is 9(x + 2).

In the given word phrase, "a number" is represented by the variable x. The phrase "two more than a number" can be translated as x + 2 since we add 2 to the number x. The phrase "the product of 9 and two more than a number" indicates that we need to multiply 9 by the value obtained from x + 2. Therefore, the algebraic expression for this word phrase is 9(x + 2).

"A number": This is represented by the variable x, which can take any value.

"Two more than a number": This means adding 2 to the number represented by x. So, we have x + 2.

"The product of 9 and two more than a number": This indicates that we need to multiply 9 by the value obtained from step 2, which is x + 2. Therefore, the algebraic expression becomes 9(x + 2).

In summary, the phrase "The product of 9 and two more than a number" can be algebraically expressed as 9(x + 2), where x represents the number.

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Adaptive Cruise Control with Cloud Connectivity Objective Use MATLA to develop and implement an adaptive cruise control system for vehicles that automatically adjusts the speed to maintain a safe distance from vehicles ahead. The speed information has to be uploaded on the cloud to support connected vehicles and intelligent transport. Hardware Arduino uno x 1, button x 5, distance sensor x 1, 4 digit 7-segment anode display x 1 Description Implement an adaptive cruise control system using the Arduino UNO board. The system is controlled by five buttons of (1) Set_speed, (2) Adaptive_speed, (3) Cancel, (4) Increase_speed, and (5) Decrease_speed. After power on, the display has to show the initial speed of 0. 1. When the increase_speed button is pressed, the speed increases, and when the Decrease_speed button is pressed the speed decreases however without pressing the Set_speed button the speed will not remain constant and it changes slowly over time. 2. When the Set_speed button is pressed the system enters the cruise control mode where the speed is held constant. In this mode, the Increase_speed button and the Decrease_speed button are still functional and can be used to change the Set_speed. If the Cancel button is pressed, the system quits the cruise control mode where the speed decreases slowly. 3. If the Adaptive_speed button is pressed, the speed is set and held constant until a vehicle shows up at the front or an object is detected where the speed automatically decreases. When the road becomes clear, the speed increases to reach the set speed again. In the adaptive cruise control mode, the display has to blink to differentiate this mode from the cruise mode. In this mode, the Increase_speed button and the Decrease_speed button do not function but the Cancel button can still be used to quit the adaptive cruise mode. If the Cancel button is pressed, the display stops blinking and the vehicle speed begins to slow down. 4. The implemented system has to be able to communicate with the ThingSpeak platform to store the speed data on the cloud. ThingSpeak is an Internet of Things (IoT) application that supports MATLAB to analyze and visualize data

Answers

The objective is to develop and implement an adaptive cruise control system for vehicles using MATLAB, Arduino UNO, and ThingSpeak that automatically adjusts the speed to maintain a safe distance from vehicles ahead and uploads speed information to the cloud for connected vehicles and intelligent transport.

The system uses an Arduino UNO board, five buttons, a distance sensor, and a 4-digit 7-segment anode display. The buttons include Set_speed, Adaptive_speed, Cancel, Increase_speed, and Decrease_speed. The system has two modes, cruise control, and adaptive cruise control.

In cruise control, the speed is held constant and can be adjusted with the Increase_speed and Decrease_speed buttons. In adaptive cruise control, the speed automatically adjusts to maintain a safe distance from vehicles or objects in front and the display blinks to indicate this mode.

The system also communicates with the ThingSpeak platform to store speed data on the cloud for analysis and visualization in MATLAB.

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Let x1 > 1 and xn+1 := 2−1/xn for n ∈ N. Show that xn is bounded and monotone. Find the limit. Prove by induction

Answers

We have shown that xn is bounded and monotone increasing, and its limit is √2. First, we will show that xn is bounded and monotone increasing by induction:

Base Case: For n = 1, we have x1 > 1, which is true.

Inductive Hypothesis: Assume that xn > 1 for some n = k and show that xn+1 > xn for n = k.

Inductive Step:

We have xn+1 := 2−1/xn

Since xn > 1, we have 1/xn < 1

Therefore, 2−1/xn > 2−1/1 = 1/2

So, xn+1 > 1/2

Since xn > 1, we have xn+1 = 2−1/xn < 2−1/1/ = 1

So, 1/2 < xn+1 < 1

Therefore, xn is bounded and monotone increasing.

Next, we will find the limit of xn as n → ∞:

Let L = lim xn as n → ∞

Then, taking the limit on both sides of xn+1 = 2−1/xn, we get:

L = 2−1/L

Multiplying both sides by L, we get:

L2 = 2−1

Solving for L, we get:

L = ±√2

Since xn > 1 for all n, we have L > 1. Therefore, L = √2.

Thus, we have shown that xn is bounded and monotone increasing, and its limit is √2.

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What are the new vertices of quadrilateral KLMN if the quadrilateral is translated two units to the right and four units upward? A. K = (-2,0), L' = (1,0), M = (1,-3), N = (-2,-3) B. K = (-2,-2), L' = (1,-2), M = (1,-5), N = (-2,-5) C. K = (-0,0), L' = (3,0), M = (3,-1), N = (0,-1) D. K = (-2,2), L' = (1,2), M = (1,-1), N = (-2,-1)

What are the new vertices of quadrilateral KLMN if the quadrilateral is translated two units to the right

Answers

K' ( -2, 2) , L' (1,2) , M' (1,-1) , N' (-2,-1)

Firstly, we needt to identify the coordinates of the vertices of the quadilateral

Afterwards, we then perform the translation

The translation simply means we add 2 to the x-value and add 4 to the y-value

So if we had coordinates of a vertex as (x,y); upon translation, we will have (x + 2, y+ 4)

Let us identify the vertices;

K'

K (-4,-2)

L (-1,-2)

M (-1,-5)

N (-4,-5)

After translation, we have;

K' ( -2, 2) , L' (1,2) , M' (1,-1) , N' (-2,-1)

A professor at a local university noted that the exam grades of her students were normally distributed with a mean of 73 and a standard deviation of 11. The professor has informed us that 8. 75 percent of her students received grades of a. What is the minimum score needed to receive a grade of a?.

Answers

The minimum score needed to receive a grade of A is 88.51

Let, X, be the scores of the student's

X follows Normal Distribution with mean = μ = 73 and standard deviation = σ = 11

The professor has informed us that 7.93 percent of her students received grades of A.

That is  P( X > a ) = 7.93% = 0.0793 .

We have to find a.

P( X > a ) = 7.93% = 0.0793

So, P( X <=  a ) = 1 - 0.0793 = 0.9207

Using function = NORMINV( probability , μ ,σ )

a = NORMINV( 0.9207, 73 , 11 ) = 88.51

The minimum score needed to receive a grade of A is 88.51

We have to find P( X <= 57.93 )

Using function = NORMDIST( x, μ , σ , 1 )

P( X <= 57.93 ) =NORMDIST( 57.93 , 73 , 11 , 1 ) = 0.0853 = 8.53%

8.53 percent of students failed the course

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Use the Ratio Test to determine the convergence or divergence of the series. If the Ratio Test is inconclusive, dete INFINITY, respectively.) 00 n 31 n = 1 an + 1 = lim n

Answers

To determine the convergence or divergence of the series using the Ratio Test, we need to evaluate the limit of the ratio of consecutive terms as n approaches infinity.

Using the formula given, we have:
an+1 = (3n+1)/(n³+1)
an = (3n-2)/(n³+1)
So, we can write the ratio of consecutive terms as:
an+1/an = [(3n+1)/(n³+1)] / [(3n-2)/(n³+1)]
an+1/an = (3n+1)/(3n-2)
Now, taking the limit of this expression as n approaches infinity: lim (n→∞) [(3n+1)/(3n-2)] = 3/3 = 1

Since the limit is equal to 1, the Ratio Test is inconclusive. Therefore, we need to use another test to determine the convergence or divergence of the series. However, we can observe that the series has the same terms as the series ∑1/n² which is a convergent p-series with p=2. Therefore, by the Comparison Test, we can conclude that the series ∑(3n-2)/(n³+1) also converges. In summary, the series ∑(3n2)/(n³+1) converges.

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what is the value of x in 5x−3(x−11)=7(2x−5)+2

Answers

The value of x is 5.5. I got this answer by first distributing -3 amongst (x-11), and distributing 7 amongst (2x-5). Next I combined like terms and subtracted 3x from 5x, and added -35 and 2. Next I subtracted 33 from both sides. Next I subtracted 14x from both sides. And finally I divided both sides by -12 to get the final answer of 5.5.
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