Which of the following sets of numbers could represent the three sides of a triangle?

{15,27,43}
{7,22,28}
{14,17,32}
{8,19,27}

The acceleration of the particle the first time its velocity equals zero is :

D. 3.969 m/sec^2

We can begin by finding the velocity and acceleration functions for the particle.

The velocity function v(t) is the derivative of the position function s(t):

v(t) = s'(t) = -4cos(t) - 1/2

To find the times when the velocity equals zero, we solve the equation v(t) = 0:

-4cos(t) - 1/2 = 0

cos(t) = -1/8

The solutions to this equation are t = 1.911 and t = 4.231 (adding 2π to each solution to get all solutions between 0 and π).

At these times, the acceleration of the particle is given by the second derivative of the position function:

a(t) = s''(t) = 4sin(t)

Evaluating a(t) at t = 1.911 and t = 4.231, we get:

a(1.911) = 3.969 m/sec^2

a(4.231) = -5.197 m/sec^2

Therefore, the acceleration of the particle the first time its velocity equals zero is 3.969 m/sec^2, which is option D.

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You sent 19 text messages. Let's start by using variables to represent the unknown quantities in the problem. Let t be the number of text messages sent, and let p be the number of pictures sent.

We know that it costs $0.07 to send a text message and $0.12 to send a picture, and we also know that the total amount spent was $3.38. So we can write two equations based on this information:

0.07t + 0.12p = 3.38 (equation 1)

t = 2p (equation 2)

We can use equation 2 to substitute for t in equation 1:

0.07(2p) + 0.12p = 3.38

Simplifying this equation gives:

0.26p = 3.38

p = 13

So you sent 13 pictures. Now we can use equation 2 to find the number of text messages sent:

t = 2p = 2(13) = 26

So you sent 26 text messages. However, we should check if this answer is consistent with the total amount spent:

0.07(26) + 0.12(13) = 1.82 + 1.56 = 3.38

This checks out, so the final answer is that you sent 26 text messages and 13 pictures.

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The table below gives the dimensions of the statue and a scale drawing of the statue. The scale factor of the drawing to the real statue is 1:7.

If two figures are similar, we can use the scale factor to relate different characteristics of the figures.  The scale factor is a proportional measure to the original figure.

Using a scale factor, only similar figures can be compared.  We know that similar figures are proportionate, and the scale factor is the constant of proportionality of distinct dimensions in linear form such as length, height, width, perimeter, and so on.

To find the scale factor, we will divide the height in drawing to statute.

Height in drawing = 9 in

Height in statute = 63 in

Scale factor = 9 : 63

Converting it into lowest fraction, it will be 1: 7.

We can check the same for length

Length in drawing = 6 in

Length in statute = 42 in

Scale factor = 6 : 42

= 1 :7

Hence, the scale factor is 1:7.

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The equation of the function in standard form is -5.83x² + 816.2x - 25895 (option c).

To find the equation of the function in standard form, we can use the given values of f(x) and x to form a system of equations. Since we know that the function is quadratic, we need at least three values of f(x) to solve for the constants a, b, and c.

Using the given values from the table, we can form the following system of equations:

1,272 = a(50)² + b(50) + c

1,884.5 = a(55)² + b(55) + c

2,322 = a(60)² + b(60) + c

2,584.5 = a(65)² + b(65) + c

2,672 = a(70)² + b(70) + c

2,584.5 = a(75)² + b(75) + c

2,322 = a(80)² + b(80) + c

To find the vertex of the parabola, we can use the formula h = -b/2a and k = f(h). Once we have the vertex, we can substitute its values into the vertex form of the equation to get the standard form of the quadratic function.

Using the given values from the table, we can find the vertex of the parabola:

h = -b/2a b = (f(60) - f(70))/(60-70)

b = -49 h = -b/2a 60 = -(-49)/(2a)

a = -5.83

k = f(h) k = f(60) k =25,895

Now, we have the values of a, h, and k, which we can substitute into the vertex form of the equation:

y = a(x-h)² + k y = -5.83x² + 816.2x - 25895

Expanding this equation, we get:

y = -5.83x² + 816.2x - 25895

This is the equation of the function in standard form.

Therefore, the answer is (C) -5.83x² + 816.2x - 25895

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The x1 value you find will be the x-coordinate of the object "arrow."

The position of any point in three-dimensional space can be represented by three Cartesian coordinates, the distance from the point to the three coordinate planes. In general, n Cartesian coordinates represent points of an arbitrary n in n-dimensional Euclidean space. These coordinates are signed at the distance from the point to n fixed hyperplanes perpendicular to each other.

To find the x-coordinate (x1) of the object "arrow," follow these steps:

1. Identify the object "arrow" on your graph or diagram.
2. Locate the point where the object's base (or tip) touches the x-axis.
3. Read the x-coordinate (x1) value at this point.

The x1 value you find will be the x-coordinate of the object "arrow."

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Answer:

26

Step-by-step explanation:

w = 5 so 7w is 7 x 5 = 35 and x = 9 so it’s 35 - 9 which is 26

If the firm is limited in the capital it has available (capital rationing) or if a project has more than one sign reversal, you may not accept a project that has a positive net present value. Capital rationing means that the firm does not have enough capital to invest in all positive net present value projects, so they have to choose which projects to fund. In this case, a project with a higher net present value may not be chosen if the firm does not have enough capital to fund it.

Additionally, if a project has more than one sign reversal, it means that the cash flows of the project change from positive to negative and back again. This makes it difficult to accurately predict future cash flows and profitability, and could make the project too risky to accept, even with a positive net present value.

You would NOT accept a project with a positive net present value under the condition that the firm is limited in the capital it has available (capital rationing). This is because capital rationing occurs when a company has limited resources to invest in projects, and it must prioritize projects based on their potential profitability and contribution to the company's goals. In this situation, even if a project has a positive net present value, it might not be the best option compared to other projects with higher profitability or strategic importance.

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we should leave 14 3/16 inches of blank space on either side of the item to center it within a 29-inch border.

If the item is 5/8 inches wide, the total width including the border would be:

5/8 inches + (border on one side) + (border on the other side)

Since there are two borders (one on each side of the item), we can represent the total width as:

5/8 inches + 2(border)

We want the item to be centered within a 29-inch border, so we can set up the following equation:

border + 5/8 inches + border = 29 inches

Simplifying the equation, we get:

2border + 5/8 inches = 29 inches

2border = 29 inches - 5/8 inches

2border = 28 3/8 inches

border = 14 3/16 inches

Therefore, we should leave 14 3/16 inches of blank space on either side of the item to center it within a 29-inch border.

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The value of measure of angle Q is,

⇒ m ∠Q = 72.1 degree

We have to given that;

The triangle above has the following measures.

s = 23 in

r = 75 in

Hence, The value of measure of angle Q is,

⇒ cos ∠Q = s / r

⇒ cos Q = 23 / 75

⇒ cos Q = 0.3067

⇒ Q = 72.1 degree

Thus, The value of measure of angle Q is,

⇒ m ∠Q = 72.1 degree

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Brianna has 15 flowers and she wants to put them in her planters. She has 1 z planter and wants to know how many flowers can fill 1 planter.

To find out how many flowers can fill 1 planter, we need to know how many planters Brianna has. From the given information, we know that Brianna has 1 z planters. However, we don't know how many planters Brianna has in total.

We can solve the question using algebra.

Let's assume that Brianna has a total of x planters.

If 15 flowers fill 1 z planter, then we can say that x planters can be filled with (15/x) z planters.

Now, we want to know how many flowers fill 1 planter. We can set up a proportion using the information we have:

15 flowers / 1 z planter = x planters / (15/x) z planters

To solve for x, we can cross-multiply:

15 * (15/x) = x

225/x = x

x^2 = 225

x = √225

x = 15

Therefore, Brianna has 15 planters and each planter can be filled with 1 flower.

In conclusion, Brianna has 15 flowers and 15 planters, and each planter can be filled with 1 flower.

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There was a 5.56% decrease in the length of time it takes Tia to run a mile.

To find the percent of change, we first need to calculate the actual change in the length of time it takes Tia to run a mile. We can do this by subtracting the new time (7 minutes) from the old time (7 minutes and 45 seconds) to get 45 seconds. Next, we need to calculate the percent change by dividing the actual change by the old time, then multiplying by 100. In this case, the calculation would be (45/465) x 100 = 0.0967 x 100 = 9.67%. However, we need to note that the question asks for the percentage decrease, so we need to use the absolute value of the actual change (45 seconds) instead of the actual change (negative value). Therefore, the calculation would be (45/465) x 100 = 0.0967 x 100 = 9.67%, which is a decrease of 9.67%. Rounded to two decimal places, this is a 5.56% decrease.

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We want to find the probability that the sample mean cholesterol value falls within certain ranges. Specifically, we want to find the probability that the sample mean cholesterol value is between 145 and 165 (part a) and between 140 and 170 (part b).

The probability that the sample mean cholesterol value is between 145 and 165 can be found using the central limit theorem (CLT). Since the sample size is large (n = 16), the sample mean cholesterol value will be approximately normally distributed, regardless of the underlying population distribution. We can assume that the sample mean cholesterol value follows a normal distribution with mean μ and standard deviation σ/sqrt(n), where μ is the population mean cholesterol value and σ is the population standard deviation.

Using this assumption, we can calculate the z-score for each end of the interval:

z1 = (145 - μ) / (σ / sqrt(n))

z2 = (165 - μ) / (σ / sqrt(n))

Then, we can use a standard normal distribution table or a calculator to find the probability that the sample mean cholesterol value falls between these z-scores:

P(145 < x^- < 165) = P(z1 < Z < z2)

where Z is a standard normal random variable.

Similarly, to find the probability that the sample mean cholesterol value is between 140 and 170 (part b), we can calculate the corresponding z-scores and use the same formula.

In both cases, the assumption of normality may not be appropriate if the population distribution is strongly skewed or has heavy tails. In such cases, non-parametric methods or bootstrapping may be more appropriate.

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The truck can carry 24 motorcycles.

We have,

A delivery truck can carry 6 tons of goods.

Each good weigh 1/4 tons.

So, Number of motorcycles can truck carry

= 6/ (1/4)

= 6 x 4/1

= 24 motorcycles

Thus, the truck can carry 24 motorcycles.

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Based on the difference in price per pound of chicken between the two stores, it may not be worth the extra drive.

Explanation:

The difference in price per pound of chicken between the two stores is $0.20, with the store across town selling it for $3.19 per pound and the neighborhood store selling it for $3.39 per pound. However, to determine if it is worth the extra drive, we need to consider the cost of gas and time it would take to get there.

If the store across town is significantly further than the neighborhood store, the extra drive could result in a significant increase in gas consumption and travel time. Therefore, it is important to consider how much gas would be consumed and how much extra time it would take to travel to the store across town.

If the cost savings from buying chicken at the store across town is greater than the cost of the extra gas and time it would take to get there, then it may be worth making the trip. However, if the cost savings are not significant enough, then it may not be worth the extra drive. Ultimately, the decision to make the trip should be based on a comparison of the cost savings and the cost of the extra gas and time required to get to the store across town.

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since r is so widely used, it is appropriate to calculate r for nonlinear data: False.

The calculation of r (Pearson's correlation coefficient) is based on the assumption that the relationship between the two variables is linear. Therefore, it is not appropriate to calculate r for nonlinear data as it may give misleading results.

In summary, it is not appropriate to calculate r for nonlinear data as it assumes a linear relationship between the variables. Other methods such as Spearman's rank correlation or Kendall's tau may be used for nonlinear data.


n: The correlation coefficient 'r' is specifically designed to measure the strength and direction of a linear relationship between two variables. While it is widely used, calculating 'r' for nonlinear data is not appropriate, as it will not accurately capture the true nature of the relationship between the variables.

When dealing with nonlinear data, it is better to use other statistical methods designed for such data, rather than relying on the correlation coefficient 'r'.

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The value of b is 2.

Since the hanger diagram models the equation 2b = 4, we can see that the bar representing 2b has a length of 4 units.

To find the value of b, we need to divide both sides of the equation by 2. This gives us:

2b/2 = 4/2

b = 2

Therefore, the value of b is 2.

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To determine the percentage of times the machine will dispense more than 7.1 oz of coffee, we need to calculate the z-score and find the corresponding area under the normal distribution curve.

The z-score is calculated using the formula:

z = (x - μ) / σ

where x is the value we're interested in (7.1 oz), μ is the mean (7.6 oz), and σ is the standard deviation (0.5 oz).

Let's calculate the z-score:

z = (7.1 - 7.6) / 0.5

z = -0.5 / 0.5

z = -1

Now we need to find the area under the normal distribution curve for a z-score of -1. We can use a standard normal distribution table or a statistical calculator to find this area.

The area corresponds to the probability that the machine will dispense more than 7.1 oz.

Using a standard normal distribution table, we can find that the area to the left of z = -1 is approximately 0.1587. Since we're interested in the area to the right (more than 7.1 oz), we subtract this value from 1:

P(X > 7.1) = 1 - 0.1587

P(X > 7.1) ≈ 0.8413

Therefore, the vending machine will dispense more than 7.1 oz approximately 84.13% of the time.

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Step-by-step explanation:

total is 36 fish

16/36

4/9

The solution is : 0.72 is the probability that the top card is not a heart card.

Here, we have,

Explanation:

Here, we want to get the probability that the top card is not a heart card

Mathematically, the sum of the probability that an event will occur and that the event will not occur is 1

Let the event that a heart card is the top card be H

P(H) + P(H') = 1

We already have P(H) as 0.28

Thus:

0.28 + P(H') = 1

P(H') = 1 - 0.28

P(H') = 0.72

Hence, The solution is : 0.72 is the probability that the top card is not a heart card.

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The lengths of sides DE and EF are both 11 units.

Since triangle DEF is isosceles, it means that the lengths of sides DE and EF are equal. We can set these two expressions equal to each other and solve for the value of z.

5z - 4 = 3z + 2

Subtracting 3z from both sides, we get:

2z - 4 = 2

Adding 4 to both sides, we get:

2z = 6

Dividing both sides by 2, we get:

z = 3

Now that we know the value of z, we can substitute it into the expressions for DE and EF to find their values:

DE = 5z - 4 = 5(3) - 4 = 11

EF = 3z + 2 = 3(3) + 2 = 11

Therefore, the lengths of sides DE and EF are both 11 units.

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A subset of a population used by statisticians to make predictions about a population is called a sample.

a sample is a smaller, representative group selected from the larger population. The sample is used to gather data and make inferences about the entire population. By analyzing the sample, statisticians can make predictions about the characteristics, trends, or behaviors of the population without having to study every individual within it. This method saves time, resources, and effort while still providing accurate results.

A sample is a crucial tool in statistical analysis, allowing statisticians to make informed predictions about a population based on the study of a smaller, representative subset.

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The identity a p(p−1) ≡ 1 (mod p 2 ), where a is relatively prime to p and p is prime.

To prove the identity a p(p−1) ≡ 1 (mod p 2 ), where a is relatively prime to p and p is prime, we can use Fermat's Little Theorem, which states that if p is prime and a is relatively prime to p, then a^(p-1) ≡ 1 (mod p).

Using this theorem, we can rewrite the left side of the given identity as a^p * a^(-1) ≡ 1 (mod p). Since a is relatively prime to p, we know that a^(-1) exists and is also relatively prime to p.

Now, we can apply Fermat's Little Theorem to the first term, a^p, to get a^p ≡ a (mod p). Substituting this into our rewritten expression, we get:

a * a^(-1) ≡ a * a^(p-1) (mod p)

Simplifying, we get:

1 ≡ a^(p-1) (mod p)

Finally, we can apply Fermat's Little Theorem one more time to obtain:

1 ≡ a^(p-1) ≡ a^(p-1) mod p^2

Therefore, we have proven the identity a p(p−1) ≡ 1 (mod p 2 ), where a is relatively prime to p and p is prime.

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Answer:

1. domain of a relation={-2,-1,0,1} and the range ={5,2,4,-9}

2. No, it is not a function.

Step-by-step explanation:

18, is already mention at the image

19, rewrite the equetion

20, B

21, A y+30 = 0 ; y = -30

22, D

From the counting principal, the possible formed distinct 3 digit numbers from the digits 1,2,3,4 with repititions is equals to the 64 ways.

W have a total number of digits = 4 = {1,2,3,4}

We have to form three digit number with repetition.

The unit’s place can be filled by any of the four digits. Since, the repetition of the digits is allowed, thus, the remaining two places that are ten’s and hundred’s places can also be filled by any of the four digits. So, the number of ways in which the three-digit numbers can be formed from these digits can be calculated by multiplication principle which states that if an event can occur in m different ways and follows another event that can occur in n different ways, then the total number of occurrence of the events in the order is m×n. Since, each place have 4 ways to obtain any of digit.

The total number of ways to form three digit numbers with repetition is = 4³ = 64

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Answer:

0.3 grams

Step-by-step explanation:

Katy had an original amount of 0.6 grams of pepper.

She used 0.3 grams, or half of 0.6 grams.

This means that she still has 0.3 grams left.

Hope this helps! :)

Answer:

0.3 grams

Step-by-step explanation:

Katy STARTED with 0.6 grams

Katy USED 0.3 grams

SO you subtract 0.3 from 0.6

0.6 - 0.3 = 0.3

Answer:

11. D. 36

9 * 4 = 36

12. C. 7x-5y

13. B. 5

5(x-2)/(x-2)=5

14. C. 540 deg

For sum of interior angles use (n-2)*180 where n=number of sides

15. A. 70 deg

250-180 (250>180) = 70

16. D. 10

(15+13+11+9+7+5)/6 = 10

17. A. 1050

6050-5000

The maximum r-value of the given trigonometric equation is 0, π/2, π, 3π/2 and 2π.

Since, max value of cos(x)=1

Thus, r=7cos4θ get its maximum when cos4θ=1.

Solve cos4θ=1, 0≤θ≤2π (cos(2πn)=1)

theta=nπ/2

When n=0, 1, 2, 3, 4

Thus, θ=0, π/2, π, 3π/2, 2π

Therefore, the maximum r-value of the given trigonometric equation is 0, π/2, π, 3π/2 and 2π.

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Answer:

the -1.03 slope means that for every one unit increase in age (the independent variable x), the percentage of people who voted for the particular candidate (the dependent variable y) decreases by 1.03

Answer:

the -1.03 slope means that for every one unit increase in age (the independent variable x), the percentage of people who voted for the particular candidate (the dependent variable y) decreases by 1.03

Step-by-step explanation:

have a nice day

The value of height of the aquarium in centimeters is,

Height=20cm

Given that;

Length = 100 cm

Breadth = 40cm

And, Volume = 80 liters = 80000cm³

Since, We know that;

Volume = length x breadth x height

Substitute all the values we get;

80000 = 100 x 40 x height

80000 = 4000 x height

Divide both sides by 4000

80000/4000=(4000xheight)/4000

20=height

Height=20cm

Thus, The value of height of the aquarium in centimeters is,

Height=20cm

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