What is the product written in scientific notation? (5.91×10−3)⋅(8.7×1010)

Answer:

The answer is 6a+2b

Step-by-step explanation:

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Final answer:

Kara will pay $55.68 for the dress after a 15% discount is applied to the original price of $65.50.

Explanation:

Kara wants to buy a dress with an original price of $65.50, and there is a 15% discount on it.

To find out how much Kara will pay for the dress after the discount, we first need to calculate the amount of the discount.

To do this, we convert the percentage to a decimal by dividing by 100 (15% = 0.15) and then multiply it by the original price of the dress.

The amount of the discount is:

$65.50 × 0.15 = $9.825.

To find out the final price that Kara pays, we subtract the discount from the original price:

$65.50 - $9.825 = $55.675.

However, stores usually round the price to the nearest cent, so Kara would pay $55.68 for the dress after the discount is applied.

The statement is option (A) ∠ ADB and ∠CBD satisfies the alternate interior angle theorem.

A rectangle is one of the types of quadrilaterals in which all four angles are right angles or equal to 90 degrees. It is four-sided polygon in which the opposite sides are parallel and equal to each other.

For the given situation,

The diagram below shows the rectangle ABCD.

The diagonals AC and BD are drawn.

From the diagram,

According to alternate interior angle theorem, [tex]\angle ADB[/tex] and [tex]\angle CBD[/tex] are alternate interior angles .

Hence we can conclude that the statement is option (A) ∠ ADB and ∠CBD satisfies the alternate interior angle theorem.

Learn more about the rectangles here

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Answer: -1/3

Step-by-step explanation:

Slope is the difference between the y coordinate points divided by the x coordinate points

We have (-1, 2) and (-4, 3)

Slope = 3 - 2/ -4 - (-1)

Slope = -1/3

(X+3)^2-x^2=39  x^2+6X+9-x^2=39 6x+9=39. 6x=30 x =5 x+3=8

Answer:

Her centripetal acceleration during the turn at each end of the track is [tex]0.432\, \frac{m}{s^{2}}[/tex]

Step-by-step explanation:

Total distance covered in one round , D= 400 m

Time taken to cover one round , T = 1 min 40 s = 100 sec

Speed of runner , [tex]V=\frac{D}{T}=\frac{400}{100}\, \frac{m}{s}= 4.0\, \frac{m}{s}[/tex]

Now centripetal acceleration is given by

[tex]a_c=\frac{V^{2}}{R}[/tex]

where [tex]V= 4.0\frac{m}{s}[/tex]

[tex]Radius, R= \frac{Diameter}{2}=\frac{74}{2}m=37\, m[/tex]

[tex]\therefore a_c=\frac{4^{2}}{37}\, \frac{m}{s^{2}}=0.432\, \frac{m}{s^{2}}[/tex]

Thus her centripetal acceleration during the turn at each end of the track is [tex]0.432\, \frac{m}{s^{2}}[/tex]

The centripetal acceleration of runner at each end of track is [tex]\boxed{0.432{\text{ }}{{\text{m}}\mathord{\left/{\vphantom{{\text{m}}{{{\text{s}}^{\text{2}}}}}}\right.\kern-\nulldelimiterspace}{{{\text{s}}^{\text{2}}}}}}[/tex] .

Explanation:

It is given that the diameter of oval track that consists of two half circles at each end is [tex]74{\text{ m}}[/tex] .

The distance runner runs once around the track is [tex]400{\text{ m}}[/tex] . The runner covers one round of track in [tex]1{\text{ m}}[/tex]  and [tex]40{\text{ s}}[/tex] .

Our aim is obtain the value of centripetal acceleration for runner at each track.

The expression for centripetal acceleration is shown below.

[tex]{a_c}=\frac{{{v^2}}}{R}[/tex]                                                                          …… (1)

Here, [tex]v[/tex]  is the speed of the runner and [tex]R[/tex]  is the radius of track.

The speed of the runner is the ratio of distance she takes to cover the track to the time taken by her.

The time in seconds is calculated as,

[tex]\begin{aligned}t&=60{\text{ s}}+40{\text{ s}}\\&=100{\text{ s}}\\\end{aligned}[/tex]

The distance covered is [tex]400{\text{ m}}[/tex] , so the speed calculated is shown below.

[tex]\begin{aligned}{\text{speed}}&=\frac{{{\text{distance}}}}{{{\text{time}}}}\\&=\frac{{400{\text{ m}}}}{{100{\text{ s}}}}\\&=4{\text{ }}{{\text{m}}\mathord{\left/{\vphantom {{\text{m}}{\text{s}}}}\right.\kern-\nulldelimiterspace}{\text{s}}}\\\end{aligned}[/tex]

The radius of track calculated is shown below.

[tex]\begin{aligned}R&=\frac{d}{2}\\&=\frac{{74{\text{ m}}}}{2}\\&=37{\text{ m}}\\\end{aligned}[/tex]

Substitute [tex]4[/tex]  for [tex]v[/tex]  and [tex]37[/tex]  for [tex]R[/tex]  in equation (1) to obtain the centripetal acceleration [tex]{a_c}[/tex] .

[tex]\begin{aligned}a_{c}&=\frac{(4\text{ m/s})^{2}}{37\text{ m}}\\&=\frac{16}{37}\text{ m/s}^{2}\\&=0.432\text{ m/s}^{2}\end{aligned}[/tex]

Therefore, the centripetal acceleration [tex]{a_c}[/tex]  is [tex]0.432{\text{ }}{{\text{m}}\mathord{\left/{\vphantom{{\text{m}}{{{\text{s}}^{\text{2}}}}}}\right.\kern-\nulldelimiterspace}{{{\text{s}}^{\text{2}}}}}[/tex] .

Thus, the centripetal acceleration of runner at each end of track is [tex]\boxed{0.432{\text{ }}{{\text{m}}\mathord{\left/{\vphantom{{\text{m}}{{{\text{s}}^{\text{2}}}}}}\right.\kern-\nulldelimiterspace}{{{\text{s}}^{\text{2}}}}}}[/tex] .

Learn More:

1. Centripetal Force https://brainly.com/question/6372960

2. Velocity and Momentum https://brainly.com/question/11896510

3. Centripetal force on orbit https://brainly.com/question/7420923

Answer Details:

Grade: High School

Subject: Physics

Chapter: Circular Motion

Keywords:

Track, running, diameter, circle, runner, distance, moves, constant, speed, centripetal, acceleration, force, motion, uniform, radius, velocity and oval.

x^2 +x^2 = C^2

x^2 +x^2 = 15^2

x^2 + x^2 = 225

225/2 = 112.5 = x^2

sqrt(112.5) = 10.6066

 round answer as needed

 note the answer can also be written as 15sqrt(2)/2

Final answer:

There are 27,405,5040 different ways the medals can be awarded to the 32 students.

Explanation:

In this problem, we need to find the number of different ways the 6 medals can be awarded to the 32 students. To solve this, we can use the concept of permutations. There are 32 students competing for the first medal, so there are 32 choices for that medal. Once the first medal is awarded, there are 31 students remaining to compete for the second medal, so there are 31 choices for that medal. We continue this process until all 6 medals have been awarded. Therefore, the total number of different ways the medals can be awarded is 32 * 31 * 30 * 29 * 28 * 27 = 27,405,5040.

The probability of getting exactly 3 tails when flipping a fair coin 5 times is 0.3125, or [tex]\( 31.25\% \)[/tex]. This means that in about 31.25% of the cases, when flipping a fair coin 5 times, exactly 3 of those flips will result in tails.

To find the probability of getting exactly 3 tails when flipping a fair coin 5 times, we can use the binomial probability formula. In a binomial experiment like this, where there are only two possible outcomes (heads or tails) and each trial is independent and has the same probability of success (50% for a fair coin), we can use the binomial probability formula:

[tex]\[ P(X = k) = \binom{n}{k} \times p^k \times (1-p)^{n-k} \][/tex]

Where:

- P(X = k) is the probability of getting exactly k successes (tails, in this case).

- n is the number of trials (5 flips).

- k is the number of successes (3 tails).

- p is the probability of success on each trial (0.5 for a fair coin).

- (1-p) is the probability of failure on each trial.

Substituting the given values into the formula:

[tex]\[ P(X = 3) = \binom{5}{3} \times (0.5)^3 \times (1-0.5)^{5-3} \][/tex]

[tex]\[ P(X = 3) = \binom{5}{3} \times 0.5^3 \times 0.5^2 \][/tex]

[tex]\[ P(X = 3) = \frac{5!}{3!(5-3)!} \times 0.5^3 \times 0.5^2 \][/tex]

[tex]\[ P(X = 3) = \frac{5 \times 4}{2 \times 1} \times 0.125 \times 0.25 \][/tex]

[tex]\[ P(X = 3) = 10 \times 0.125 \times 0.25 \][/tex]

[tex]\[ P(X = 3) = 0.3125 \][/tex]

So, the probability of getting exactly 3 tails when flipping a fair coin 5 times is 0.3125, or [tex]\( 31.25\% \)[/tex].

This means that in about 31.25% of the cases, when flipping a fair coin 5 times, exactly 3 of those flips will result in tails.

Proving that PR = QS

Therefore, PR = QS

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The greatest number of weights the trainer can purchase is 17.

To find the maximum number of weights the trainer can purchase, we need to divide the trainer's total budget by the cost of each weight.

Step 1: Find the cost of weights per trainer's budget: $156 - $78 = $78

Step 2: Divide the cost of weights by the cost of each weight: $78 / $4.50 = 17.33

Since you cannot purchase a fraction of a weight, the trainer can purchase a maximum of 17 weights.