The original selling price of a jacket was s dollars. The selling price was then changed on two occasions by the store owner. Its price is now represented by 0. 85 (1. 4s). Which expression could explain what happened to the price of the jacket?

The maximum speed of the sprinter during the race is estimated to be approximately 12.72 meters per second.

To calculate the maximum speed of the sprinter during the race, we need to determine the average speed over the entire distance. The formula for average speed is distance divided by time. In this case, the distance covered by the sprinter is 200 meters, and the time taken to cover this distance is 20.32 seconds.

Average Speed = Distance / Time

Average Speed = 200 meters / 20.32 seconds

Average Speed ≈ 9.84 meters per second

So, the average speed of the sprinter during the race is approximately 9.84 meters per second.

However, to find the maximum speed, we need to consider that sprinters often accelerate during a race. The sprinter's time splits of 0-5-20.32 indicate that it took the sprinter 5 seconds to cover the initial 0 meters. This suggests that the sprinter was accelerating during this period.

To estimate the maximum speed, we can calculate the average speed for the remaining 195 meters (200 meters - 5 meters).

Average Speed = Distance / Time

Average Speed = 195 meters / (20.32 seconds - 5 seconds)

Average Speed ≈ 195 meters / 15.32 seconds

Average Speed ≈ 12.72 meters per second

Therefore, the maximum speed of the sprinter during the race is estimated to be approximately 12.72 meters per second. It's important to note that this is an estimate based on the given information, and actual maximum speeds achieved by athletes can vary based on various factors such as training, technique, and race conditions.

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Answer: 28 wands

Step-by-step explanation:

Answer:

2 wands

Step-by-step explanation:

I hope this helps!

Step-by-step explanation:

for x=5

3×0+5-5=0

0+0=0

i don't know i just tried

Answer:

  C.  142°

Step-by-step explanation:

You want the angle between vectors u=3i+√3j and v=-2i-5j.

There are a number of ways the angle between the vectors can be found. For example, the dot-product relation can give you the cosine of the angle:

  u•v = |u|·|v|·cos(θ) . . . . . . where θ is the angle of interest

You can find the angles of the vectors individually, and subtract those:

  u = |u|∠α

  v = |v|∠β

  θ = α - β

When the vectors are expressed as complex numbers, the angle between them is the angle of their quotient:

  \(\dfrac{\vec{u}}{\vec{v}}=\dfrac{|\vec{u}|\angle\alpha}{|\vec{v}|\angle\beta}=\dfrac{|\vec{u}|}{|\vec{v}|}\angle(\alpha-\beta)=\dfrac{|\vec{u}|}{|\vec{v}|}\angle\theta\)

This method is used in the calculation shown in the first attachment. The angle between u and v is about 142°.

A graphing program can draw the vectors and measure the angle between them. This is shown in the second attachment.

__

Additional comment

The approach using the quotient of the vectors written as complex numbers is simply computed using a calculator with appropriate complex number functions. There doesn't seem to be any 3D equivalent.

The dot-product relation will work with 3D vectors as well as 2D vectors.

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Answer:

1.2

Step-by-step explanation:

The cost per pound is $2.3.

Given that Bo is buying candy by the pound. For every 10 pounds, he pays $23.

We need to find the cost per pound,

So, we see that,

For 10 pounds he is paying $23,

We need to find the unit rate, so divide both by 10,

10/10 pound = $23/10

1 pound = $2.3

Hence the cost per pound is $2.3.

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Answer:

11.66

Step-by-step explanation:

10^2 + 6^2 = Z^2

100 + 36 = Z^2

136 = Z^2

sqrt(136) = Z

sqrt 136 = 11.66

Answer:

= { 1, 2, 4, 4, 8, 10, 12, 14}

There are total 8 numbers in data. so,

two middle numbers are : 4, 8

= 4+8

= 12

now divide 12 with 2

= 6

So... the median of given set is 6.

Answer:

7

Step-by-step explanation:

since there are two middle numbers you add and divide them by 2

Answer:

Since the graph of a certain quadratic function has no x-intercepts, the discriminant has to be negative, so A and D are possible values for the discriminant.

The third term and fourth term has a sum of 108.

Let's use the formula for the nth term of an exponential sequence:

\(a_n = a_1 * r^{(n-1)}\)

where \(a_1\) is the first term, r is the common ratio, and n is the term number.

We're given that the second term is 9, so we know:

\(a_2 = a_1 * r = 9\)

We're also given that the fourth term is 81, so we know:

\(a_4 = a_1 * r^3 = 81\)

We can use the equation for \(a_2\) to solve for \(a_1\):

\(a_1 * r = 9\\a_1 = 9 / r\)

Substituting this expression for \(a_1\) into the equation for \(a_4\), we get:

\((9 / r) * r^3 = 81\\r^2 = 9\\\)

r = 3 or r = -3

Since we have a common ratio, we can find the third term using either value of r:

\(a_3 = a_2 * r = 9 * 3 = 27\)

Now we can find the sum of the third and fourth terms:

\(a_3 + a_4 = 27 + 81 = 108\)

Therefore, the sum of the third term and fourth term is 108.

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Using the hypergeometric distribution, it is found that there is a 0.5714 = 57.14% probability that he chooses two different types of biscuits.​

The formula is:

\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}\)

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

The parameters are:

In this problem, the values of the parameters are given as follows:

N = 7, k = 3, n = 2.

The probability that he chooses two different types of biscuits is P(X = 1), hence:

\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}\)

\(P(X = 1) = h(1,7,2,3) = \frac{C_{3,1}C_{4,1}}{C_{7,2}} = 0.5714\)

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Answer:

3?

Step-by-step explanation:

3n²+4m+5

3n²+(4m+5)

=3n²+9m

=3n²/9m;(3÷9)(n²÷m)

=1n²/3m

=n²/3m

The term U describes the incenter of the given triangle.

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

STR is a given triangle.

Let us understand the differences between Orthocenter, Incenter, Centroid and Circumcenter.

Circumcenter is the point of which is equidistant from all the vertices of the triangle.

Incenter is the point of which is equidistant from the sides of the triangle.

Orthocenter is the point at which all the altitudes of the triangle intersect.

centroid is the point of intersection of the medians of the triangle.

By observing this we can tell that U is the incenter of the triangle RST.

Hence, the term U describes the incenter of the given triangle.

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Answer:

a<-2

Step-by-step explanation:

a < 1-3

a < -2

< does not have a line underneath so it'll be an open circle.

The arrow should be pointing to the right.

Sentence Set A: Argument with conclusion "Have you no common decency?" Sentence Set B: Not an argument. Sentence Set C: Argument with conclusion "Dr. Sullivan, how could you possibly suggest giving my husband a painful cancer treatment when he has only two weeks to live?" Sentence Set D: Not an argument.

Sentence Set A is an argument because it presents a series of statements aimed at persuading or challenging someone's behavior. The first two sentences express the speaker's emotional response to the way they are being spoken to and the potential hurt caused by it.

The final sentence, "Have you no common decency?" serves as the conclusion of the argument, implying that the person being addressed should consider their actions and exhibit basic manners.

Sentence Set B, on the other hand, does not form an argument.

While it discusses the speaker's frustration with outdated reference materials at the library and proposes an alternative solution of doing research online, it lacks a clear claim or conclusion that presents a logical appeal or challenge to persuade others.

In Sentence Set C, an argument is made against Dr. Sullivan's suggestion of a painful cancer treatment for the speaker's husband. The statements express concerns about the potential lack of success of the treatment and the additional suffering it may cause during the final two weeks of the husband's life.

The conclusion is formed by the initial question: "Dr. Sullivan, how could you possibly suggest giving my husband a painful cancer treatment when he has only two weeks to live?"

Sentence Set D does not constitute an argument as it involves an expression of surprise and disappointment regarding someone's math skills, but it lacks a clear claim or conclusion that presents a logical challenge or persuasive appeal.

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The complete question is:

Sentence Set A:

S1: Don't ever speak to me like that again.

S2: Don't you know how much it hurts my feelings when you talk to me like that?

S3: Have you no common decency?

Sentence Set B:

S1: I'm so tired of having to go to the library to do my research.

S2: Can you believe that half of the reference materials I found there last time were outdated?S3: Let's just tear down the library and do our research online from now on.

Sentence Set C:

S1: Dr. Sullivan, how could you possibly suggest giving my husband a painful cancer treatment when he has only two weeks to live?

S2: What if the treatment isn't successful?

S3: Would you want your spouse to suffer even more during her final two weeks?

Sentence Set D:

S1: How could you possibly have got x = 5 as your answer?

S2: Didn't you see that y = 47?

S3: I have never seen such sloppy math in my entire life.

Which of the sentence sets are arguments? If applicable, what is the conclusion of each argument?

Answer:

The answer is 21

Step-by-step explanation:

6+6 bc the other side is the same as the one that has 6. 6+6+9=21

The probability that the student chosen will be a boy who watched tennis yesterday is 1/8.

Given that 56 students were asked if they watched tennis yesterday, 20 of the students are boys, 17 girls watched tennis yesterday and 32 students did not watch tennis yesterday and out of all these one students is to be chosen at random.

We have to find the probability that the student chosen will be a boy who watched tennis yesterday.

Total number of students is 56.

The total number of girls is 56-20=36

Girls who didn't watch tennis is 36-17=19

Number of the boys who did not watch the game is 32-19=13

Number of boys watching a tennis match is 20-13=7

Now, we will find the probability that the student chosen will be a boy who watched tennis yesterday.

Probability=Number of boys watching a tennis match/Total number of students
Probability=7/56

Probability=1/8

Hence, the probability that the student chosen will be a boy who watched tennis yesterday when 56 students were asked if they watched tennis yesterday is 1/8.

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Answer:

-3, -2.4, -2 1/4, -1.5, -1 1/8

Step-by-step explanation:

Hope this helps! Let me know if you have any questions! (also would you mind putting me as brainliest pls?)

Answer:

-3, -2.4, -2 1/4, -1.5, -1 1/8

Step-by-step explanation:

I took test

Answer:

2(p - 32)(p + 2)

Step-by-step explanation:

2p² - 60p - 128 ← factor out common factor 2 from each term

= 2(p² - 30p - 64) ← factor the quadratic

consider the factors of the constant term ( - 64) which sum to give the coefficient of the p- term (- 30)

the factors are - 32 and + 2 , since

- 32 × + 2 = - 64 and - 32 + 2 = - 30 , then

p² - 30p - 64 = (p - 32)(p + 2) , so

2p² - 60p - 128 = 2(p - 32)(p + 2)

The factors of a quadratic equation 2p² - 60p - 128 are (p - 4) and (p - 32).

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. In other terms, a "polynomial function of degree 2" is a quadratic function.

To factorize a quadratic equation of the form ax² + bx + c, we need to find two numbers that multiply to ac and add up to b. In this case, we have:

a = 2, b = -60, c = -128

The product of a and c is:

ac = 2 × (-128) = -256

We need to find two numbers that multiply to -256 and add up to -60. We can start by listing the factors of -256:

1, -1, 2, -2, 4, -4, 8, -8, 16, -16, 32, -32, 64, -64, 128, -128, 256, -256

We can see that -16 and 16 are a pair of factors that multiply to -256. We can also see that -16 + 16 = 0, which is not what we want. We need factors that add up to -60, not to 0.

We can try the next pair of factors, -32 and 8. These multiply to -256 and add up to -24. This is closer to what we want, but we need factors that add up to -60.

We can try the next pair of factors, -64 and 4. These multiply to -256 and add up to -60. This is what we need, so we can use these factors to factorize the quadratic equation:

2p² - 60p - 128 = 2(p - 4)(p - 32)

Therefore, the factors of the quadratic equation are (p - 4) and (p - 32).

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Time taken by Miguel car to drive is, 1.6 hour.

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

We have to given that;

Miguel went for a drive in his new car. He drove at a speed of 53 miles per hour for 84.8 miles.

We know that;

⇒ Speed = Distance / Time

⇒ Time = Distance / Speed

Here, Speed = 53 miles per hour

Distance = 84.8 miles

Hence, We get;

⇒ Time = 84.8 / 53

⇒ Time = 1.6 hour

Thus, Time taken by Miguel car to drive is, 1.6 hour.

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The length of the side AC is 2x and this can be determined by using the sine function which is an important trigonometric function.

Given :

Given side AB in triangle ABC has length x.

The trigonometric function can be used to determine the length of the side AC. Sine function can be used to determine the length of AC.

The sine function is the ratio of the opposite side to the hypotenuse. The sine function is given by:

\(\rm sin\theta = \dfrac{Opposite }{Hypotenuse}\)

Now, put the known values in the above equation.

\(\rm sin30^\circ = \dfrac{x}{AC}\)

\(\rm \dfrac{1}{2}=\dfrac{x}{AC}\)

AC = 2x

So, the correct option is D).

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The investment will double in nine years at an interest rate of approximately 8.09% compounded annually.

To find the value of the (P/A,8%,145) factor, we can use the general formula for the present worth of an annuity:

(P/A, i%, n) = (1 - (1 + i)^(-n)) / i

Substituting the values given:

i = 8%

n = 145

(P/A,8%,145) = (1 - (1 + 0.08)^(-145)) / 0.08

Using a financial calculator or spreadsheet software, we can calculate the value of (P/A,8%,145) as follows:

(P/A,8%,145) ≈ 43.7276 (rounded to four decimal places)

Therefore, the correct choice for the value of (P/A,8%,145) is:

C. (P/A,8%,145) = (P/A,8%,100)(P/A,8%,45) ≈ 43.7276 (rounded to four decimal places)

Regarding the second question, to find the interest rate at which an investment will double in nine years, we can use the future worth factor formula:

(F/P, i%, n) = (1 + i)^n

We want the investment to double, so we have:

(1 + i)^9 = 2

Taking the ninth root of both sides:

1 + i = 2^(1/9)

Solving for i:

i ≈ 0.0809 or 8.09% (rounded to two decimal places)

Therefore, the investment will double in nine years at an interest rate of approximately 8.09% compounded annually.

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Answer:     9 is the next number of this series. Similarly, apply thus rule. 9×2=18 and 18+9=27. Next is 27.

Step-by-step explanation:

Since the equation does not hold for n = 1 and n = 2, it does not hold for all positive integers n.

(i) Proving the given statement:

Using the definition of Θ:

Let f(n) = 1∗11+3∗17+5∗23+…+(2n−1)(6n+5), then

f(n) = Θ(n³).

Now, we have to prove 1∗11+3∗17+5∗23+…+(2n−1)(6n+5)=4n³+8n²−n for all positive integers n.

For n = 1, 1(6(1) + 5) = 4 + 8 - 1.

LHS = 11 and RHS = 11.

Hence the equation is true for n = 1.

Now assume that the equation is true for n = k.

1∗11+3∗17+5∗23+…+(2k−1)(6k+5)=4k³+8k²−k ----------- (1)

Now, let's prove for n = k + 1.

1∗11+3∗17+5∗23+…+(2k+1)(6k+11)=4(k+1)³+8(k+1)²−(k+1)

Putting k + 1 in place of k in equation (1),

1∗11+3∗17+5∗23+…+(2k+1)(6k+11)=4k³+12k²+8k+4+8k²+16k+8−(k+1)1∗11+3∗17+5∗23+…+(2k+1)(6k+11)

                                                   =4k³+12k²+8k+4+8k²+16k+8−k−11∗11+3∗17+5∗23+…+(2k+1)(6k+11)

                                                   =4k³+12k²+8k+4+8k²+16k+8−k−1+1LHS = 1∗11+3∗17+5∗23+…+(2k−1)(6k+5) + (2k+1)(6k+11)

                                                   = f(k) + (2k+1)(6k+11)

RHS = 4k³+8k²−k + 4k²+12k+4+4k³+12k²+8k+1

       = 8k³+24k²+20k+5

       = 4(k+1)³+8(k+1)²−(k+1)

Hence proved.

(ii) Disproving the given statement:

Let's assume that the statement is true for all positive integers n.

Let's put n = 1 in the given equation,

1+22∗2−1​+2∗33∗3−2​+3∗44∗4−3​+…+n(n+1)(n+1)∗(n+1)−n​=n+1−n+11​1 + 2.1/2 + 2.1/6 - 1 + ... + (n(n+1)/(n+1)² - n)

                                                                                        = 1

Now, let's put n = 2 in the given equation.

1+22∗2−1​+2∗33∗3−2​+3∗44∗4−3​+…+n(n+1)(n+1)∗(n+1)−n​=n+1−n+11​1 + 2.1/2 + 2.1/6 - 1 + 2.2/3 + 3.3/8 - 2 + ... + (2.3/9 - 2)

                                                                                        = 2/3

Since the equation does not hold for n = 1 and n = 2, it does not hold for all positive integers n.

Hence disproved.

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Answer:

11.7

Step-by-step explanation:

(−7.8)(−1.5)

Hope ths helps

Answer:

38

Step-by-step explanation:

Hope this helps!!

Answer:

the answer to the question is 12cm

Answer:

16 cups

Step-by-step explanation:

In order to find the answer to this question we need to solve it using what we know about unit measurements.

3 cups = 12 oz

\(12\div 3 = 4\)

1 cup = 4 oz

1lb = 16 oz

\(4\times4=16\)

4 cups = 1lb

16 cups = 4lb

=16 cups

Hope this helps.

The average value of the function f(x) = (x + 2) on the interval [0, 3] is 7/2.

Calculate the definite integral of the function over the interval [a, b], then divide it by the interval's length (b - a), in order to determine the average value of a function f(x) over the interval.

Given that the interval is [0, 3] and the function f(x) = (x + 2), we have:

= (1/3) × [1/2 x² + 2x] evaluated from x=0 to x=3

= (1/3) × [(1/2 × 3² + 2×3) - (1/20² + 20)]

= (1/3) × [(9/2 + 6) - 0]

= (1/3) × (21/2)

= 7/2

Therefore, the average value of the function f(x) = (x + 2) on the interval [0, 3] is 7/2.

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Hey there! I'm happy to help!

Numbers with the same variable and exponent are like terms and can be simplified.

\(2y^5+4y^5=6y^5\)   (variable is y, exponent is 5)

\(-3y^3-5y^3=-8y^3\) (variable is y, exponent is 3)

So, our final simplified form is \(6y^5-8y^3\).

Have a wonderful day! :D

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