Rita bought a pair of jeans for $89. The sales-tax rate is 11 percent. What is the total amount she paid for the jeans?

Answer:

Option (2) is correct graph.

Step-by-step explanation:

Given:

The function to graph is given as:

[tex]f(x)=4(\frac{1}{2})^x[/tex]

Now, the above function is an exponential function of the form [tex]f(x)=ka^x[/tex]

Where, 'k' and 'a' are constants.

The range of an exponential function is always greater than 0.

The domain is all real numbers.

Now, for graphing it, we need to find some points on it and its end behaviour.

Now, for x = 0, the function value is given as:

[tex]f(0)=4(\frac{1}{2})^0=4[/tex]

So, (0, 4) is a point on the graph.

Now, for x = 1, the function value is given as:

[tex]f(1)=4(\frac{1}{2})^1=4\times\frac{1}{2}=2[/tex]

So, (1, 2) is another point on the graph.

Now, for x = 2, the function value is given as:

[tex]f(2)=4(\frac{1}{2})^2=4\times\frac{1}{4}=1[/tex]

So, (2, 1) is another point on the graph.

Now, as 'x' tends to ∞, the function value tends to:

[tex]f(x\to\infty)=4\cdot\frac{1}{2}^{\infty}=\frac{4}{\infty}=0[/tex]

So, as

[tex]x\to\infty,f(x)\to0\\\\x\to-\infty,f(x)\to\infty[/tex]

Now, from among all the options, only option (2) fulfills all the conditions given above.

So, option (2) is correct graph.

Answer:

option 2

Step-by-step explanation:

To solve the programming task, you would create a loop to read integers, use a counter to track consecutive duplicates and print the count after a negative number is entered to end the input.

The student's question involves writing a piece of code that reads a sequence of non-negative integers, ends the input with a negative integer, and reports the number of consecutive duplicate values entered before the negative integer is encountered. This is a programming task that typically involves a loop and a counter.

To address this question, you would write a loop that continues to accept input until a negative number is entered. Inside the loop, you would use a counter to keep track of the number of consecutive duplicates. Here is a pseudocode example:

Initialize the previous Value to None (or some value that won't occur in the sequence).

Initialize the count Of Duplicates to 0.

Start a loop that reads integers until a negative number is encountered.

Inside the loop, compare the current number to the previous Value.

If they are the same, increment the count Of Duplicates by 1.

Set the previous Value to the current number before the next iteration.

Outside the loop, print count Of Duplicates.

The counter pattern is a fundamental concept in programming that is used to tally occurrences within iteration structures like loops.

Answer:

Step-by-step explanation:

I'm going to use calculus to solve this, because it's the simplest way.  

The acceleration due to gravity in feet is the second derivative of the position function.  We will start with the acceleration and work backwards with antiderivatives to get to the position function.

a(t) = -32.  Going backwards and using the fact that the initial vertical velocity is 64 ft/sec, our velocity function is

v(t) = -32t + 64.  Going backwards and using the fact that the initial height of the ball is 6 feet, our position function is

[tex]s(t)=-16t^2+64t+6[/tex]

The first part of this question asks us the maximum height of the ball.  From Physics, we learn that the maximum height of a projectile is reached when the velocity is 0, which happens to be right where the projectile stops for a nanosecond in the air to turn around and come back down.  We set the velocity function equal to 0 and solve for t.

0 = -32t + 64 and

0 = -32(t - 2).  By the Zero Product Property, either -32 = 0 or t - 2 = 0.  It's obvious that -32 does not equal 0, so t - 2 must equal 0.  Solving this for t:

t - 2 = 0 so

t = 2 seconds.  Since the maximum height is reached at a time of 2 seconds, we plug 2 seconds into the position function to get its position at 2 seconds (which is also the max height of the ball).

[tex]s(2)=-16(2)^2+64(2)+6[/tex] and

s(2) = -64 + 128 + 6 so

s(2) = 70 feet

Now we want to know when the ball will hit the ground.  "When" is a time value, and we know that the height of the ball on the ground is 0, so we sub in a 0 for s(t) and factor the quadratic.

Using the quadratic formula:

[tex]t=\frac{-64+/-\sqrt{4096-4(-16)(6)} }{-32}[/tex] and

[tex]t=\frac{-64+/-\sqrt{4480} }{-32}[/tex] which gives us the 2 solutions

[tex]t=\frac{-64+\sqrt{4480} }{-32}[/tex] and

[tex]t=\frac{-64-\sqrt{4480} }{-32}[/tex]

Plugging into your calculator, the first t = -.0916500 and the second t = 4.091

We all know that time cannot ever be negative, so our t value is 4.09.

Again, from Physics, we know that a projectile reaches it max height at halfway through its travels, so it just goes to follow logically that if it halfway through its travels at 2 seconds, then it will hit the ground at 4 seconds.  And it does!! How awesome is that?!

The maximum height of the ball is 32 feet. The ball will hit the ground after 4 seconds.

To find the maximum height of the ball, we can use the equation for motion under constant acceleration.

The equation is h = (v0^2)/(2g),

where h is the maximum height, v0 is the initial vertical velocity, and g is the acceleration due to gravity.

Plugging in the given values, we have h = (64^2)/(2*32), which gives us a maximum height of 32 feet.

Next, to find when the ball will hit the ground, we can use the equation for time of flight.

The equation is t = (2v0)/g, where t is the time of flight.

Plugging in the given values, we have t = (2*64)/32, which gives us a time of flight of 4 seconds.

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Answer:

25.15 ponds is the weight of two year old baby corresponds to 10th percentile.      

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 29 pounds

Standard Deviation, σ = 3 pounds

We are given that the distribution of weight of two year old babies is a bell shaped distribution that is a normal distribution.

Formula:

[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]

We have to find the value of x such that the probability is 0.10

P(X < x)  

[tex]P( X < x) = P( z < \displaystyle\frac{x - 29}{3})=0.10[/tex]  

Calculation the value from standard normal z table, we have,  

[tex]P(z < -1.282) = 0.10[/tex]

[tex]\displaystyle\dfrac{x - 29}{3} = -1.282\\x = 25.154 \approx 25.15[/tex]

Thus, 25.15 ponds is the weight of two year old baby corresponds to 10th percentile.

Answer:

Measurement of all angle= [tex]76.79\º+102.66\º+15.35\º+265.16\º= 360\º[/tex]

Step-by-step explanation:

Given angles are [tex]x\º, (\frac{5x}{9} +60)\º, (\frac{x}{5} )\º, (4x-142)\º[/tex]

The given is a quardilateral.

We know the sum of all angles of quardilaterals is 360º

∴ [tex]x\º+ (\frac{5x}{9} +60)\º+ (\frac{x}{5} )\º+(4x-142)\º= 360\º[/tex]

Now, solving the equation to find value of x.

⇒ [tex]x\º+ (\frac{5x}{9} +60)\º+ (\frac{x}{5} )\º+(4x-142)\º= 360\º[/tex]

Opening parenthesis.

⇒ [tex]x\º+ \frac{5x}{9} +60\º+ \frac{x}{5} \º+4x-142\º= 360\º[/tex]

⇒ [tex]5x\º+ \frac{5x}{9} + \frac{x}{5} \º-82\º= 360\º[/tex]

Adding both side by 82

⇒ [tex]5x+ \frac{5x}{9} + \frac{x}{5} = 442[/tex]

Taking LCD 45

⇒ [tex]\frac{45\times 5x+ 5\times 5x+9x}{45} = 442[/tex]

Multiplying both side by 45

⇒ [tex]225x+25x+9x= 19890[/tex]

⇒[tex]259x= 19890[/tex]

Dividing both side by 259

⇒[tex]x= \frac{19890}{259}[/tex]

∴[tex]x= 76.79\º[/tex]

Next subtituting the value of x to find measurement of other interior angle.

[tex]x\º, (\frac{5x}{9} +60)\º, (\frac{x}{5} )\º, (4x-142)\º[/tex]

2. [tex](\frac{5x}{9} +60)\º[/tex]

= [tex]\frac{5\times 76.79}{9} +60= 42.66+ 60[/tex]

= [tex]102.66\º[/tex]

3. [tex](\frac{x}{5} )\º[/tex]

= [tex](\frac{76.79}{5} )\º= 15.35\º[/tex]

4. [tex](4x-142)\º[/tex]

= [tex]4\times 76.79- 42= 307.16-42[/tex]

= [tex]265.16\º[/tex]

Question is Incomplete,Complete question is given below;

At a college, the cost of tuition increased by 10%. Let b be the former cost of tuition. Use the expression b + 0.10b for the new cost of tuition.

a)  Write an equivalent expression by combining like terms.

b)  What does your equivalent expression tell you about how to find the new cost of tuition?

Answer:

a. The equivalent expression is [tex]1.1b[/tex].

b. The new cost of tuition is 1.1 times the former cost of tuition.

Step-by-step explanation:

Given:

Former cost of tuition = [tex]b[/tex]

the cost of tuition increased by 10%.

New cost of tuition = [tex]b+0.10b[/tex]

Solving for part a.

we need to find the equivalent expression by combining the like terms we get;

Now Combining the like terms we get;

new cost of tuition = [tex]b(1+0.1) = 1.1b[/tex]

Hence The equivalent expression is [tex]1.1b[/tex].

Solving for part b.

we need to to say about equivalent expression about how to find the new cost of tuition.

Solution:

new cost of tuition = [tex]1.1b[/tex]

So we can say that.

The new cost of tuition is 1.1 times the former cost of tuition.

The question is about identifying a reaction mechanism based on the provided rate law, which is derived from the reactant concentrations. A likely mechanism is a single-step process where the reactants come together to form the product, mirroring the rate law's implication that reactant concentration directly influences the reaction rate.

The student is asking about the mechanism of a reaction and its rate law. In chemistry, the rate law expresses the relationship among the reaction rate, the reaction mechanism, and the concentrations of the reactants.

The provided rate law is rate = k[x2y2][z2], which suggests that the reaction is first order with respect to both x2y2 and z2. A plausible mechanism for this reaction would involve a single step where one molecule of each reactant comes together to form the product, 2x2y2z.

In a single-step mechanism, the rate law is derived directly from the stoichiometry of the reactants in the balanced chemical equation. Since the rate law matches the stoichiometry of the reactants, it is likely that this could represent an elementary reaction, given that the stoichiometry and the rate law coincide.

The direct relationship implied by the rate law between the concentration of the reactants and the reaction rate can be explained by the likelihood of reactant particles colliding and reacting being greater with increased concentrations, a concept fundamental in kinetics.

Answer:

Correct answer choices are [tex]27x^{2}[/tex] and [tex]657 cm^{2}[/tex]

Step-by-step explanation:

We are able to arrive at these answers through basic equation used to calculate area of an triangle and monomial laws

The average rate of change for the function over the interval 1 ≤ x ≤ 3 is 2.

The average rate of change for a function can be calculated by finding the difference in the function values over the given interval and dividing it by the difference in the x-values over the same interval.

For the given function graphed, the average rate of change over the interval 1 ≤ x ≤ 3 is calculated as follows:
Average rate of change = (f(3) - f(1)) / (3 - 1)

By evaluating the function at x = 1 and x = 3 and applying the formula, we find:
Average rate of change = (6 - 2) / 2 = 4 / 2 = 2

Therefore, the BEST estimate of the average rate of change for the function over the interval 1 ≤ x ≤ 3 is 2 (option A).

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Answer:

61.12 units²

Step-by-step explanation:

(½ × pi × r²) + (½ × b × h)

½ [(3.14 × 4²) + (8 ×9)]

½(122.24)

61.12 units²

Answer:

61.13 units squared

Step-by-step explanation:

This figure is composed of a semicircle and a triangle. Let's find these areas separately:

1) SEMICIRCLE:

The area of a semicircle is: [tex]A=\frac{\pi r^2}{2}[/tex] , where r is the radius (which is the distance from the center to a point on the circle). In this case, the radius of the circle is 4. So, we have:

[tex]A=\frac{\pi *4^2}{2} =\frac{16\pi }{2} =8\pi[/tex] ≈ 25.13 units squared

2) TRIANGLE:

The area of a triangle is: [tex]A=\frac{bh}{2}[/tex] , where b is the base and h is the height. Here, the base is 8 (b = 8) and the height is 9 (h = 9). So, we have:

[tex]A=\frac{8*9}{2} =\frac{72}{2} =36[/tex] units squared

Finally, we add these two areas together:

25.13 + 36 = 61.13 units squared.

Hope this helps!

Answer: the salesperson earns $54 as commission.

Step-by-step explanation:

A furniture salesperson earns 4.5% commission on every piece of furniture sold. The salesperson sells a sofa for $1000. This means that the commission that he earned from the sale of the sofa is

4.5/100 × 1000 = 0.045 × 1000 = $45

The salesperson also sold a chair for $200. This means that the commission that he earned from the sale of the chair is

4.5/100 × 200 = 0.045 × 200 = $9

The total commission that the salesperson earns is

45 + 9 = $54

Answer:

The probability of selecting a non-defective part provided by supplier A is 0.807.

Step-by-step explanation:

Let A = a part is supplied by supplier A, B = a part is supplied by supplier B and D = a part is defective.

Given:

P (D|A) = 0.05, P(D|B) = 0.09

A supplies four times as many parts as B, i.e. n (A) = 4 and n (B) = 1.

Then the probability of event A and B is:

[tex]P(A)=\frac{n(A)}{n(A)+N(B)}= \frac{4}{4+1}=0.80\\P(B)\frac{n(B)}{n(A)+N(B)}= \frac{1}{4+1}=0.20[/tex]

Compute the probability of selecting a defective product:

[tex]P(D)=P(D|A)P(A)+P(D|B)P(B)\\=(0.05\times0.80)+(0.09\times0.20)\\=0.058[/tex]

The probability of selecting a non-defective part provided by supplier A is:

[tex]P(A|D')=\frac{P(D'|A)P(A)}{P(D')} = \frac{(1-P(D|A))P(A)}{1-P(D)}\\=\frac{(1-0.05)\times0.80}{(1-0.058)}\\ =0.80679\\\approx0.807[/tex]

Thus, the probability of selecting a non-defective part provided by supplier A is 0.807.

The required probability of selecting a non-defective part provided by supplier A is 0.807.

Let,

A part is supplied by supplier A,

B part is supplied by supplier B,

And D = a part is defective.

Given:

P ([tex]\frac{D}{A}[/tex]) =5% = 0.05,

P([tex]\frac{D}{B}[/tex]) = 9% =  0.09

A supplies four times as many parts as B, .

Then, n (A) = 4 and n (B) = 1.

The probability of event A and B is:

Probability of event P(A) = [tex]\frac{n (A)}{n (A) + n(B)}[/tex] = [tex]\frac{4}{4+1}[/tex]

                                 P(A) = [tex]\frac{4}{5}[/tex]

And Probability of Event P(B) = [tex]\frac{n (B )}{n (A) + n(B)} = \frac{1}{4+1}[/tex]

                                        P(B) = [tex]\frac{1}{5}[/tex]

Then , the probability of selecting a defective product:

P(D) = [tex]P(\frac{D}{A}) P(A) + P(\frac{D}{B}) P(B)[/tex]

P(D) = 0.50×0.80 + 0.09×0.20

P(D) = 0.058

The probability of selecting a non-defective part provided by supplier A is

[tex]P(\frac{A}{D'} )= \frac{P(D'(A)) . P(A)}{P(D')} \\\\[/tex]

          = [tex]\frac{1- P(D(A)). P(A)}{1-P(A)} \\\\\frac{(1-0.05) . 0.80}{1- 0.05} \\\\[/tex]

          = 0.807

Hence, the probability of selecting a non-defective part provided by supplier A is 0.807.

For more information about Probability click the live given below.

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Each chef at "sushi emperor" prepares 15 regular rolls and 20 vegetarian rolls daily. On tuesday, each customer ate 2 regular rolls & 3 vegetarian rolls. by the end of the day, 4 regular rolls & 1 vegetarian roll remained uneating. how many chefs were on tuesday ? and how many customers were they ?

There were 2 chefs and 13 customers on tuesday

Let x be the number of chefs at Sushi Emperor and y be the number of customers on Tuesday.

From given,

Each chef prepares 15 regular rolls and 20 vegetarian rolls daily

If each chef prepares 15 regular rolls, then x chefs prepare 15x regular rolls

If each customer ate 2 regular rolls, then y customers ate 2y regular rolls

By the end of the day, 4 regular roll remained un eating

Therefore,

15x - 2y = 4 --------- eqn 1

If each chef prepares 20 vegetarian rolls, then x chefs prepare 20x vegetarian rolls

If each customer ate 3 vegetarian rolls, then y customers ate 3y vegetarian rolls

By the end of the day, 1 vegetarian roll remained uneating

Therefore,

20x - 3y = 1 ---------- eqn 2

Let us solve eqn 1 and eqn 2

Multiply eqn 1 by 3

45x - 6y = 12 ------- eqn 3

Multiply eqn 2 by 2

40x - 6y = 2 ------- eqn 4

Subtract eqn 4 from eqn 3

45x - 6y = 12

40x - 6y = 2

( - ) --------------

5x = 10

x = 2

Substitute x = 2 in eqn 1

20(2) - 3y = 1

40 - 3y = 1

3y = 39

y = 13

Thus there were 2 chefs and 13 customers

Answer: the equations are

b + d = 8

6x + 5y = 43

Step-by-step explanation:

Let b represent the number of hours that Julia babysits.

Let d represent the number of hours she walks dogs.

Julia worked for a total of 8 hours babysitting and walking the dogs.. This means that

b + d = 8

Julia earns $6 an hour babysitting and earns $5 an hour walking dogs. She earned a total of $43 after working a total of 8 hours at her two jobs. This means that

6x + 5y = 43

Answer:

Only one person is in the stopped vehicle

Step-by-step explanation:

Answer:

The answer to your question is below

Step-by-step explanation:

a) The intervals in which the graph is decreasing are the right section of the first parabola, the left section of the second parabola and also the right section of the third parabola.

               (9, 11) U (14.5, 17) U (21, 27)

b) There are only two intervals in which the graph is increasing

                (1, 9) U (17, 21)

c) During the time the graph is increasing, Andre is getting away from his origin.

Answer:

not a function - it does not pass the vertical line test.

Step-by-step explanation:

Answer:

Step-by-step explanation:

1) since the sixth term is 3 and the fifth term 24, the common ratio would be 3/24 = 1/8

The formula for finding the nth term of a geometric sequence is

Tn = ar^(n - 1)

If t6 = 3,r = 1/8, then

3 = a × 1/8^(6 - 1) = a × (1/8)^5

a = 3/(0.125)^5 = 98304

The first term is 98304.

Second term is 98304 × 1/8 = 12288

Third term is 12288 × 1/8 = 1536

Third term is 1536 × 1/8 = 192

2) t1 = 4

t2 = - 3t(2- 1) = - 3t1 = - 3 × 4 = - 12

t3 = - 3t(3- 1) = - 3t2 = - 3 × - 12 = 36

t4 = - 3t(4- 1) = - 3t3 = - 3 × 36 = - 108

3) let the numbers be t2,t3 and t4

The sequence becomes

1/2, t2,t3, t4,8

The formula for finding the nth term of a geometric sequence is

Tn = ar^(n - 1)

8 = 1/2 × r^(5 - 1)

8 = 1/2 × r^4

16 = r^4

2^4 = r^4

r = 2

t2 = 1/2 × 2 = 1

t3 = 1 × 2 = 2

t4 = 2 × 2 = 4

Answer:

A cross-section that is perpendicular to the base of a cube.

A cross-section that is perpendicular to the base of a cylinder whose base diameter and height are the same.

Step-by-step explanation:

We have to select from options that the two-dimensional cross section are squares.

The correct options are :

A cross-section that is perpendicular to the base of a cube.

A cross-section that is perpendicular to the base of a cylinder whose base diameter and height are the same.  

In both the cases the length and the width of the section are equal. (Answer)

Among the given options, only the cross-section that is perpendicular to the base of a cube is guaranteed to be a square. The other options will generally result in different shapes, such as triangles or circles.

The question asks which two-dimensional cross sections are squares. To find the answer, we must consider the shape of the object and the orientation of the cross section.

At first glance, only the cross-section perpendicular to the base of a cube is a square. However, depending on specific conditions not typically met by the listed shapes, other cross-sections can appear square-shaped. Therefore, generally, the answer is a cross-section that is perpendicular to the base of a cube will be square.

Answer:

14 gums.

Step-by-step explanation:

Given: Jacob bought 13 pack of gum

           He already had 5 piece of gum.

           He shared gum with six of his friends.

           Each one of them received 27 pieces of gum.

Lets assume the number of gums in each pack be "x".

Total number of gum= [tex]number\ of\ gum\ in\ each\ pack\times number\ of\ pack + 5[/tex]

Also gum has been shared among jacob and his 6 friends, which is 7 person.

∴ Share of each person= [tex]\frac{Total\ number\ of\ gums}{number\ of\ person}[/tex]

Now, forming equation to find number of gums in each pack.

⇒ [tex]\frac{13\times x+5}{7} = 27[/tex]

Multiplying both side by 7

⇒ [tex]13x+5= 189[/tex]

Subtracting both side by 5

⇒ [tex]13x= 189-5[/tex]

⇒[tex]13x= 184[/tex]

Dividing both side by 13

⇒ [tex]x= \frac{184}{13}[/tex]

∴[tex]x= 14.15 \approx 14\ gum[/tex]

Hence, each pack have 14 gums.

Final answer:

The question is a mathematical problem where we find that Devon has 70 points after setting up and solving an algebraic equation based on the conditions given.

Explanation:

The student's question revolves around a Mathematical problem concerning the points scored by two players, Erin and Devon, in a game. Erin has 42 points, and the question provides a condition that if Devon had 14 more points, he would have double the points Erin has. This scenario can be translated into an algebraic equation to solve for the number of points Devon currently has.

Let's denote the current number of points Devon has as D. According to the problem, if Devon had 14 more points, his total would be D + 14. We are also told that this hypothetical total would be double the points Erin has, which is 42. Therefore, we can write the equation as:

D + 14 = 2 × 42

By solving this equation, we can find out how many points Devon has:

Devon currently has 70 points.

Erin has 42 points. Devon has 70 points. If he had 14 more, he'd have double Erin's points.

let's break it down step by step:

Given:

- Erin has 42 points.

- If Devon had 14 more points, he'd have double the points Erin has.

Let's denote Devon's points as [tex]\( D \).[/tex]

According to the given information, if Devon had 14 more points, he'd have double the points Erin has. So, mathematically, we can represent Devon's points as [tex]\( 2 \times 42 \)[/tex] when we add those 14 points.

So, we can write the equation:

[tex]\[ D + 14 = 2 \times 42 \][/tex]

Now, let's solve for [tex]\( D \):[/tex]

[tex]\[ D + 14 = 84 \][/tex]

Subtract 14 from both sides of the equation:

[tex]\[ D = 84 - 14 \]\[ D = 70 \][/tex]

So, Devon currently has 70 points.

Answer:

There are 7 dogs.

Step-by-step explanation:

7 (dogs) x 7 (biscuits) = 49

3 (cats) x 6 (biscuits) = 18

49 + 18 = 67

Step-by-step explanation:

average rate of change of function is given by :

[tex]f= (f(a+h)-f(a))/h[/tex]

where

[tex]f(x)=3x[/tex]

and a= 7

so inserting values is formula for h=1

[tex]f=(f(7+1)-f(7))/1[/tex]

[tex]f= f(8)-f(7)= 3(8)-3(7)=24-21=3[/tex]

now for h= 0.1

[tex]f=(f(7+0.1)-f(7))/0.1=(f(7.1)-f(7))/0.1=(3(7.1)-3(7))/0.1[/tex]

[tex]f=3[/tex]

similarly average rate of change of given function is same for all given step sizes.

Final answer:

The question involved calculating the average rate of change of the function f(x) = 3x over various intervals, showing that the rate of change is constant and equals 3 for all given values of h.

Explanation:

The question asks to calculate the average rate of change of the function f(x) = 3x over the intervals [a, a + h] for values of h = 1, 0.1, 0.01, 0.001, and 0.0001, where a = 7.

The average rate of change is calculated using the formula [tex]\frac{f(a+h) - f(a)}{h}[/tex]

For each value of h, we substitute a and h into the function and use the formula to find the average rate of change.

For h = 1, the average rate of change is 3.

For h = 0.1, the average rate of change is also 3.

For h = 0.01, the average rate of change remains 3.

For h = 0.001, the average rate is again 3.

Similarly, for h = 0.0001, the average rate of change is 3.

Using technology for values of h smaller than 0.1 is recommended due to the precision required in calculations. However, for this particular function, the rate of change is constant across these intervals, simplifying the process.

To calculate the time spent above 40 meters on a Ferris wheel, we analyze the wheel's structure and use trigonometry to find the proportional time of the ride corresponding to the arc above the 40-meter mark.

Calculating Time Spent Above 40 meters on a Ferris Wheel

To determine how many minutes of the ride on the Ferris wheel are spent higher than 40 meters above the ground, we need first to understand the wheel's structure and motion. Given that the Ferris wheel has a diameter of 50 meters and is boarded from a platform 4 meters above the ground, we can calculate the highest and lowest points riders will reach during the ride. The highest point of the wheel will be 50 meters (the radius) plus 4 meters (the platform height), totaling 54 meters. The lowest point will be 4 meters (platform height) above the ground since the diameter is equal to twice the radius and the wheel's lowest point touches the platform level.

Because riders want to be above 40 meters, we're interested in the segment of the ride where they are between 40 meters and the maximum of 54 meters above the ground. This range covers a portion of the wheel's circumference. If the wheel's highest point is at 12 o'clock and the loading platform is at 6 o'clock, then the 40-meter height will be somewhere between 6 o'clock and 12 o'clock.

Using the fact that the Ferris wheel completes one revolution in 4 minutes, we can find the time spent over 40 meters by calculating the angle θ that corresponds to the arc between 40 meters and 54 meters above the ground. The 40-meter height will fall at the point where the vertical distance from the top of the wheel equals the wheel's radius minus 40 meters. Using this, we can use trigonometry to find θ, and then convert this angle to a proportion of the full revolution time to determine the time spent on this segment of the ride.

Answer: B.  [tex]\dfrac{28}{55}[/tex] .

Step-by-step explanation:

Given : Number of blue disks =4

Number of green disks = 8

Total disks = 12

Total number of combinations of drawing any 3 disks from 12 = [tex]^{12}C_3[/tex]

Number of combinations of drawing 1 blue and 2 green disks = [tex]^{4}C_1\times^{8}C_2[/tex]

Now , the probability that 1 of the disks selected is blue, and 2 of the disks selected are green will be :

[tex]\dfrac{^{4}C_1\times^{8}C_2}{^{12}C_3}\\\\=\dfrac{4\times\dfrac{8!}{2!6!}}{\dfrac{12!}{3!9!}}\\\\=\dfrac{4\times28}{220}\\\\=\dfrac{28}{55}[/tex]

Hence, the correct answer is B.  [tex]\dfrac{28}{55}[/tex] .

Answer:

(a) At 5% significance level, reject H0

At 1% significance level, reject H0

(b) At 5% significance level, fail to reject H0

At 1% significance level, fail to reject H0

Step-by-step explanation:

(a) The test is a one tailed test

At 5% significance level, the critical value is 1.645

Conclusion: Reject H0 because the test statistic -1.78 is less than the critical value 1.645

At 1% significance level, the critical value is 2.326

Conclusion: Reject H0 because the test statistic -1.78 is less than the critical value 2.326

(b) The test is a two tailed test

At 5% significance level, the critical value is 1.96. The region of no rejection of H0 lies between -1.96 and 1.96

Conclusion: Fail to reject H0 because the test statistic -1.78 falls within -1.96 and 1.96

At 1% significance level, the critical value is 2.576. The region of no rejection of H0 lies between -2.576 and 2.576

Conclusion: Fail to reject H0 because the test statistic falls within -2.576 and 2.576

The conclusion that can be made from an hypothesis test depends on

the significance level and p-value.

Response:

(a) The conclusion at 5% is there is statistical evidence to suggest that p < 0.65

At 1% level; fail to reject H₀: p = 0.65, there is statistical evidence to suggest that p = 0.65

(b) With Hₐ ≠ 0.65, the conclusion at the 5% significance level is that there is sufficient statistical evidence that p = 0.65

At the 1% level, fail to reject H₀: p = 0.65,

The null hypothesis, H₀: p = 0.65

The alternative hypothesis, Hₐ: p < 0.65

The z-score is z = -1.78, which gives;

The p-value = 0.0375

(a) The significance level is 5%

Which gives, α = 0.05

Given that the p-value is less than the significant level, we have that

there is sufficient evidence against the null hypothesis, given that the

probability that the null hypothesis is correct is less than the significant

level of 5%.

Therefore, reject H₀, p = 0.65

However, at 1% significant level, α = 0.01, and the p-value, p = 0.0375 is

larger than the significance level.

(b) Hₐ: p ≠ 0.65

We have;

[tex]\alpha = \dfrac{5 \%}{2} = 2.5 \% = \mathbf{0.025}[/tex]

Which gives;

The p-value (0.0375) is larger than the significant level, therefore, we

fail to reject the null hypothesis.

At the 1% level of significance, we have;

[tex]\alpha = \dfrac{1 \%}{2} = 0.5 \% = 0.005[/tex]

Which gives;

The p-value at z = -1.78 (p = 0.0375) is larger than the significant level

Therefore;

Learn more about hypothesis testing here:

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Final answer:

To determine the angle of elevation of the sun, calculate the inverse tangent (arctan) of the height of the tower (106 feet) divided by the length of its shadow (141 feet). The angle of elevation is approximately 37 degrees to the nearest degree.

Explanation:

To find the angle of elevation of the sun given that a 106 feet tall tower casts a shadow of 141 feet long, we can use trigonometry. Specifically, the tangent of the angle, which is the ratio of the opposite side (the height of the tower) to the adjacent side (the length of the shadow).

We use the formula:

tangent of angle = opposite / adjacent

Tan(angle) = 106 / 141

Now we need to calculate the inverse tangent (arctan) of this ratio to find the angle in degrees:

Angle = arctan(106/141)

After performing this calculation with a calculator or using a trigonometric table, we find that the angle to the nearest degree is approximately 37 degrees.

Answer:

$88812.33

Step-by-step explanation:

Principal = $89,000

But there's a sales tax of 4.2%

Tax = (4.2 / 100) * 89000 = $3738

Total cost of the mobile house = $89000 + $3738 = $92,738

However, they made a down payment of $3000

Balance after down payment = $92,738 - $3000 = $89,738

They've also paid the first monthly payment of $925.67

Balance after first monthly payment =

$89,738 - $925.67 = $88,812.33

The principal balance after applying there first monthly payment is $88,812.33

The principal balance, after applying the first month's payment of $925.67 to an initial loan of $89,738 for a mobile home, is $88,812.33.

To calculate the principal balance after the first month’s payment, start by adding the initial price of the mobile home and the sales tax. The sales tax is 4.2% (or 0.042) of $89,000, which comes out to $3,738. Then, subtract the down payment from the sum to get the initial loan amount. So, $89,000 + $3,738 - $3,000 equals $89,738. After applying the first month’s payment of $925.67, subtract that amount from the initial loan, leaving a principal balance of $88,812.33.

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Answer:

True

Step-by-step explanation:

Statistics is indeed a procedure consists of collection, presentation, analysis and presentation of the data. Statistics is widely used in every field of life. For example we want to assess the performance of students. For this purpose we choose a sample of students and ask about their grading. This is the procedure of collection of data. Then this data can be presented in tabular form or graphical form and this stage is known as presentation of the data. Then we evaluate their average and this procedure is known as analysis of data. Then according to average we make statement about performance of students and this stage is interpretation of the data.

Answer: 61.9°

Approximately: 62°

Step-by-step explanation:

Using Pythagoras

(AC)^2 = 17^2 - 15^2

= 289 - 225

√AC = √64

AC = 8

Cos C = Adj/ Hyp

Cos C = 8/17

Cos C = 0.4706

Inverse of Cos C

C = 61.93°

Approximately: 62°