20.7 rounded off to the nearest tens place

Answer: The distance between these two points is 5.

Step-by-step explanation:

Yay! Love doing distance formula questions!

Okay, so first off, the distance formula goes as follows:

d = \(\sqrt(x^{2} - x^1)^2 + (y^{2}-y^1)^2\)

Basically you just plug in your coordinates to the formula.

Step 1:

\(\sqrt(-5 + 5)^{2} + (2-7)^{2}\)

Step 2: Distribute the exponent to both parenthesis to get \(\sqrt{25}\).

Step 3: Factor the number, which would result in \(\sqrt{5^2}\).

As a result of this, your answer would be 5.

The price of the TV when purchased online and at the superstores will be $325 and $350, respectively. The cost of the TV at the online retailer is cheaper.

The amount of any product is given as though it was a proportion of a hundred.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

Television from the manufacturer costs $250. A 30% markup is typical for an online shop, whereas a 40% markup is typical for a superstore.

The price of the TV when purchased online is given as,

⇒ $250 x 1.30

⇒ $325

The price of the TV when purchased at the superstores is  given as,

⇒ $250 x 1.40

⇒ $350

The cost of the TV at the online retailer is cheaper.

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The positive difference between the sum of the first 15 positive even numbers and the sum of the first 15 positive odd numbers is 15.

We are supposed to find out the positive difference between the sum of the first 15 positive even numbers and the sum of the first 15 positive odd numbers. That means we need to find the sum of the first 15 positive even numbers and the sum of the first 15 positive odd numbers separately and then find their positive difference.

Step 1: Calculation of the sum of the first 15 positive even numbers: Even numbers are multiples of 2 and first 15 even numbers are 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30. The sum of the first 15 positive even numbers is equal to (2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20 + 22 + 24 + 26 + 28 + 30). The sum can be calculated as follows :sum of the first 15 positive even numbers = 2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20 + 22 + 24 + 26 + 28 + 30= 240

Step 2: Calculation of the sum of the first 15 positive odd numbers: Odd numbers are not multiples of 2 and first 15 odd numbers are 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29. The sum of the first 15 positive odd numbers is equal to (1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23 + 25 + 27 + 29). The sum can be calculated as follows: sum of the first 15 positive odd numbers = 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23 + 25 + 27 + 29= 225

Step 3: Calculation of positive difference between the sum of the first 15 positive even numbers and the sum of the first 15 positive odd numbers: We have found that the sum of the first 15 positive even numbers is 240 and the sum of the first 15 positive odd numbers is 225. Thus, the positive difference between the sum of the first 15 positive even numbers and the sum of the first 15 positive odd numbers is equal to the absolute difference between 240 and 225.Positive difference = |240 - 225|= 15. Thus, the positive difference between the sum of the first 15 positive even numbers and the sum of the first 15 positive odd numbers is 15.

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Answer:

2 x or 3x

Step-by-step explanation:

because is have x

Answer:

x = 30

Step-by-step explanation:

The sum of the exterior angle and interior angle of a polygon = 180°

Then the 2 unknown interior angles are

180 - 2x and 180 - (3x - 20) = 180 - 3x + 20 = 200 - 3x

The sum of the 4 interior angles of a quadrilateral = 360°

sum the 4 interior angles and equate to 360

2x + 2x + 10 + 180 - 2x + 200 - 3x = 360 , that is

- x + 390 = 360 ( subtract 390 from both sides )

- x = - 30 ( multiply both sides by - 1 )

x = 30

The solution to the inequality, 1/2x - 3 < -1 3/8, is x < 13/4. See the graph below.

Given the inequality, 1/2x - 3 < -1 3/8, solve to find the value of x, which is the solution to the inequality.

1/2x - 3 < -1 3/8 [given]

1/2x - 3 < -11/8

Add 3 to both sides of the equation:

1/2x - 3 + 3 < -11/8 + 3 [addition property of equality]

1/2x < 13/8

Multiply both sides by 2:

1/2x * 2 < 13/8 * 2 [multiplication property of equality]

x < 13/4

The solution to this inequality, x < 13/4 is given in the graph below.

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The probability that a randomly selected group of 16 individuals from the campus will be selected is 0.8023 or 80.23%

Based on the sign in the elevator of the college library, the limit of 16 persons and weight limit of 2,500 pounds need to be adhered to. To ensure compliance with both limits, we need to consider both the number of people and their weight.

Assuming that the distribution of weights of individuals on campus is approximately normal with an average weight of 155 pounds and a standard deviation of 29 pounds, we can use this information to estimate the total weight of a group of 16 randomly selected individuals.

The total weight of a group of 16 individuals can be estimated as follows:

Total weight = 16 x average weight = 16 x 155 = 2480 pounds

To determine if this total weight is within the weight limit of 2,500 pounds, we need to consider the variability in the weights of the individuals. We can do this by calculating the standard deviation of the total weight using the following formula:

Standard deviation of total weight = square root of (n x variance)

where n is the sample size (16) and variance is the square of the standard deviation (29 squared).

Standard deviation of total weight = square root of (16 x 29^2) = 232.74

Using this standard deviation, we can calculate the probability that the total weight of the group of 16 individuals is less than or equal to the weight limit of 2,500 pounds:

Z-score = (2,500 - 2,480) / 232.74 = 0.86

Using a standard normal distribution table or calculator, we can find that the probability of a Z-score less than or equal to 0.86 is approximately 0.8023.

Therefore, the probability that a randomly selected group of 16 individuals from the campus will comply with both the number and weight limits in the elevator of the college library is approximately 0.8023 or 80.23%.

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Answer:

B.) A & B

Step-by-step explanation:

For example x^2-64= (x+8)(x-8)

The two figures shown are made of unit squares. The positive difference of the perimeters, in units, is 8.

Perimeter is the total distance around the boundary of the shape. Since each square has a side length of 1 unit, the perimeter is equal to the number of sides.

1. Figure A: Counting the number of unit squares on the boundary of the shape, the perimeter of the first shape is:   8+4+4+4+4=24 units.

2. Figure B:Counting the number of unit squares on the boundary of the shape, the perimeter of the second shape is: 10+2+10+2=24 units.

The positive difference of the perimeters in units = |24 - 24| = 0 units. Therefore, the positive difference of the perimeters, in units is 0.

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Answer:

\(\huge\boxed{\sf x = 3}\)

Step-by-step explanation:

According to intersecting chord theorem, if two chords intersect each other, the product of lengths of each chord will be equal.

Such that,

\(a \times b = c \times d\)

\(x \times 2 = 1 \times 6\\\\2x = 6\\\\Divide \ both \ sides \ by \ 2\\\\x = 6/2\\\\x = 3\\\\\rule[225]{225}{2}\)

Answer:

D

Step-by-step explanation:

2x + 3 > -9

2x > -12

x > -6

Choice D represents x > -6

Answer: i think its the last one but if not then the second to last

Step-by-step explanation:

Answer:

(x + 6)(x + 7)

Step-by-step explanation:

To factor the trinomial x^2 + 13x + 42, we need to find two numbers that multiply to 42 and add up to 13.

One way to do this is to list all the pairs of factors of 42 and see which pair adds up to 13:

1, 42 -> 1 + 42 = 43

2, 21 -> 2 + 21 = 23

3, 14 -> 3 + 14 = 17

6, 7 -> 6 + 7 = 13

So the pair of factors that we want is 6 and 7. We can use these numbers to rewrite the middle term of the trinomial:

x^2 + 13x + 42 = x^2 + 6x + 7x + 42

Next, we can group the first two terms and the last two terms:

x^2 + 6x + 7x + 42 = (x^2 + 6x) + (7x + 42)

Now, we can factor out the greatest common factor from each group:

x(x + 6) + 7(x + 6)

Notice that we have a common factor of (x + 6) in both terms. We can factor this out:

(x + 6)(x + 7)

The time is needed between injections is 3.6 hours, i.e., the drug is to be injected again when the number of milligrams reaches 6 mg.

We have the exponential function of number of milligrams D (ht) of a certain drug that is in a patient's bloodstream h hours after the drug is injected is

\(D(h)=25 {e}^{ - 0.4 h}\)

We have to solve for h (the numbers of hours) that would have passed when the D(h) (the amount of medication in the patient's bloodstream) equals 6 mg in order to know when the patient needs to be injected again.

\(6 = 25 {e}^{ - 0.4h} \)

\( \frac{6}{25} = \frac{25}{25} {e}^{ - 0.4h} \)

\(0.24= {e}^{ - 0.4h} \)

Taking logarithm both sides of above equation , we get,

\( \ln(0.24) = \ln( {e}^{ - 0.4h)} \)

Using the properties of natural logarithm,

\( \ln(0.24) = - 0.4h\)

\( - 1.427116356 = - 0.4h\)

\(h = \frac{1.42711635}{0.4} = 3.56779089\)

=> h = 3. 6

So, after 3.6 hours, the patient needs to be injected again.

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The solution to the equation 4x² + 88x = 60 by completing the square is:

x = -11 + √(136) or x = -11 - √(136)

The quadratic equation is defined as a function containing the highest power of a variable is two.

The equation is given in the question, as follows:

4x² + 88x = 60

Solving the equation by completing the square:

4x² + 88x - 60 = 0

Divide both sides by the coefficient of x² to get a leading coefficient of 1 for the x² term:

x² + 22x - 15 = 0

Take half of the coefficient of the x term, square it, and add it to both sides of the equation:

x² + 22x + (22/2)² - (22/2)² - 15 = (x + 11)² - 136= 0

Now, we can add 146 to both sides of the equation to isolate the perfect square trinomial on the left-hand side:

(x + 11)² = 136

Finally, we can take the square root of both sides to solve for x:

x + 11 = ±√(136)

x = -11 ±√(136)

So the solution to the equation 4x² + 88x = 60 is:

x = -11 + √(136) or x = -11 - √(136)

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Answer:

C.) $3.00

Step-by-step explanation:

5x + 3y = 30 - - - - - 1 x 4

3x + 4y =29 - - - - - -2 x 3

--------------------------------------------

20x +12y = 120 - - - - 3

9x + 12y = 87 - - - - - 4

--------------------------------------------

3-4

20x - 9x= 120 - 87

11x = 33

X= 33

11

X = 3

hope this helps :)

The cost, in dollars, of each shirt cleaning, is $3.00 if the first customer paid $30.00 for 5 shirt cleanings and 3 pants cleaning option (C) is correct.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

Two customers went to a dry cleaner to clean their shirts and pants.

From the data given two linear equations can be framed as follows:

Let x be that each shirt cleaning costs and each pants cleaning cost the y amount.

5x + 3y = 30

3x + 4y =29

After solving the above linear equation by substitution method:

x = 3

y = 5

Thus, the cost, in dollars, of each shirt cleaning is $3.00 if the first customer paid $30.00 for 5 shirt cleanings and 3 pants cleaning option (C) is correct.

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Yes, the true mean of 33 is within the margin of error of the sample mean, we can conclude that the confidence interval does contain the true mean.

To determine whether the confidence interval contains the true mean of 33, we need to calculate the margin of error for the confidence interval. The margin of error is a measure of the precision of the estimate, and it is calculated using the sample size, the standard deviation of the population, and the desired level of confidence.

For a 95% confidence interval, the margin of error can be calculated using the following formula:

The margin of error = 1.96 * (standard deviation / √sample size)

Plugging in the values, we get:

Margin of error = 1.96 * (14 / √42)

Performing the calculation, we find that the margin of error is 3.39. This means that the sample mean of 31 is likely to be within 3.39 units of the true mean, with a confidence level of 95%.

Since the true mean of 33 is within the margin of error of the sample mean, we can conclude that the confidence interval does contain the true mean. This means that our estimate of the population mean, based on the sample size 42, is likely to be accurate.

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Answer:

x=3

Step-by-step explanation:

both of the two sides equal the same so it would be 3x=9x-18

solve you get x=3

Answer:

In explanation below.

Step-by-step explanation:

Presumably, the proof you have in mind is to use a=b=2–√a=b=2 if 2–√2√22 is rational, and otherwise use a=2–√2√a=22 and b=2–√b=2. The non-constructivity here is that, unless you know some deeper number theory than just irrationality of 2–√2, you won't know which of the two cases in the proof actually occurs, so you won't be able to give aa explicitly, say by writing a decimal approximation.

Answer:

Y=(x+10)^2-105

Step-by-step explanation:

y=x^2+20x-5

y+?=x^2+20x+?-5

y+?=x^2+20x+100-5

y+100=x^2+20x+100-5

y+100=(x+10)^2-5

y=(x+10)^2-5-100

Answer:

45 mi/h

Step-by-step explanation:

Here, we can find the total distance divided by the total time. To find the total time, we can set up 2 equations:

\(d = vt\) (which is the formula that connects velocity, time and displacement).

Here, we have to split the trip into 2 displacements because the car changes speed. So, we have 40 mi = 40 (mi/h) * t1. And t2 = 1 hour. For the second distance: 20 mi = 60 (mi/h) * t2. And t2 = 1/3 hrs.

since total time = t1+t2, we get the total time is 4/3 hours. Then, we get:

80 = \(v_{avg}\)*(4/3)  where \(v_{avg}\) is the average velocity of the trip. Finally, we get \(v_{avg}\) = 45 mi/h

Answer:

180 dollars

Step-by-step explanation:

270 for 16 hours = 16.875 dollars for each hour

15.00 an hour will be paid to larry

larry is doing 3/4 of those 16 hours

12 hours

15 x 12

larry gets 180 dollars for 12 hours of work

hope this helps x

Answer:

Step-by-step explanation:

Since there are 985 square feet to cover, and it costs 12.50 per square foot, you multiply 12.50 by 985 to get 12,312.50, the total cost and answer.

Given:

Total number of marbles = 26

Number of blue marbles = 13

Number of red marbles = 10

Number of yellow marbles = 3

To find:

The probability of getting a blue marble then a red marble (without replacement).

Solution:

Total number of marbles = 26

Number of blue marbles = 13

Probability of getting a blue marble is first draw is:

\(P(Blue)=\dfrac{\text{Number of blue marbles}}{\text{Total number of marbles}}\)

\(P(Blue)=\dfrac{13}{26}\)

\(P(Blue)=\dfrac{1}{2}\)

After drawing 1 marble, the remaining number of marbles in the bag is 25.

Probability of getting a red marble is second draw is:

\(P(Red)=\dfrac{\text{Number of red marbles}}{\text{Remaining number of marbles}}\)

\(P(Red)=\dfrac{10}{25}\)

\(P(Red)=\dfrac{2}{5}\)

Now the probability of getting a blue marble then a red marble (without replacement) is:

\(P(\text{Blue then red})=P(Blue)\times P(Red)\)

\(P(\text{Blue then red})=\dfrac{1}{2}\times \dfrac{2}{5}\)

\(P(\text{Blue then red})=\dfrac{1}{5}\)

Therefore, the probability of getting a blue marble then a red marble (without replacement) is \(\dfrac{1}{5}\).

Answer:

The answer is A and C

Step-by-step explanation:

Supplementary angles added together = 180.

Answer:

Explanation:

The statement "Suppose that 14% of people own dogs," implies that the probability of owning a dog is given as;

Therefore, if two people are selected randomly for owning dogs, they would have the same probability attached to them.

We can then combine both probabilities by using the "and" symbol. which implies "multiplication."

Workings

Answer:

When the absolute value of the scale factor is lower than 1, it decreases the size of the shape.

When the absolute value of the scale factor is greater than 1, the shape will increase in size.

How to Remember it:

Think if the number is a fraction, the shape will be a fraction of the size.

Refer to the image for the graph of the lines.

The common form of the equation of a line is y = mx + c, where m is the slope of the line and c is a constant.

We need to draw any line with a slope m = 2, and

another line with a slope m = -2.

Disclaimer: Let us assume that the constant c = 0.

Then the equation to the line with a slope of "positive" 2 is given by

y = 2x

Then the equation to the line with a slope of "negative" 2 is given by

y = -2x

Refer to the attached image for the graph of the lines with the slope of "positive" 2 and "negative" 2.

f: green line indicates a line with a slope of "positive" 2.

g: blue line indicates a line with a slope of "negative" 2.

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The probability of winning the brand new motorcycle if you buy 10 tickets is 10/1000 or 0.01, which can also be expressed as 1%.

To calculate the probability, we need to consider the total number of tickets sold and the number of tickets you purchased. In this case, there are 1000 tickets available for sale. Since you bought 10 tickets, the probability of winning is determined by the ratio of the number of tickets you bought to the total number of tickets available.

In this scenario, the probability is calculated as 10 (number of tickets you bought) divided by 1000 (total number of tickets), resulting in a probability of 0.01 or 1%.

Therefore, if you purchase 10 tickets, you have a 1% chance of winning the brand new motorcycle.

It's important to note that this probability assumes that the selection of the winning ticket is completely random and fair, with each ticket having an equal chance of being selected.

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Step-by-step explanation:

steps are in the picture.