Find the midpoint M of the line segment joining the points P=(4,-7) and Q=(-6,-3)

EXPLANATION :

From the problem, we need to select statistical questions.

Statistical questions are answered by the collection of data and there is always variability in the data.

It means that the answer must NOT have only one answer.

A. Typical amount of rainfall for the month of June, you are estimating the amount of rainfall which has many data to consider.

YES.

B. Amount of rain yesterday, since we are talking about yesterday, there's only one answer.

NO.

C. Reason why you like to listen to music. It is not answered by the data.

NO.

D. Number of songs usually the class listens to each day, we will have different answers here from day to day.

YES.

E. Number of songs did you listen to today, we are talking about today and it will have one answer only.

NO.

F. Capital of Canada, there's only one answer and it will not vary.

NO.

G. How long does it typically take for 2nd graders to walk around the track, we will have data for this since there are different rates for each 2nd grader.

YES.

ANSWER :

The statistical questions are A, D, and G

The person is approximately 8.43 miles from home, and they need to walk in the direction of approximately 26.6 degrees east of north to head directly home.

To determine the distance from home, we can use the concept of vector addition. The person walks 4 miles west, which can be represented as a vector (-4, 0) in a coordinate plane. Then, they walk 5 miles southwest, which can be represented as a vector (-3.54, -3.54) since southwest is a combination of west and south. Adding these two vectors together gives us (-7.54, -3.54).

To find the magnitude or distance from home, we use the Pythagorean theorem. The distance is given by sqrt((-7.54)^2 + (-3.54)^2) = 8.43 miles (approximately).

To determine the direction to head directly home, we need to find the angle between the vector (-7.54, -3.54) and the positive x-axis. We can use trigonometry to find this angle. The tangent of the angle is given by the ratio of the y-coordinate to the x-coordinate, which is -3.54 / -7.54. Taking the inverse tangent of this value gives us approximately 26.6 degrees.

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Answer:

22-9t

Step-by-step explanation:

(7 - 3t) + 3(-2t + 5)

=

7+−3t+(3)(−2t)+(3)(5)=

7+−3t+−6t+15

=

Now you need to combine like terms.

7+−3t+−6t+15

=

(−3t+−6t)+(7+15)=

-9t+22=

22-9t

There you go.

Answer:

22 - 9t

Step-by-step explanation:

(7 - 3t) + 3(-2t + 5)

7 - 3t + -6t + 15

7 - 9t + 15

22 - 9t

Answer:

7.6

Step-by-step explanation:

Mean = (sum of numbers)/amount of numbers

11 + 4 + 6 + 7 + 5 +10 +9 + 21 + 3 + 0 = 76

76/10 = 7.6

Answer: C

Step-by-step explanation:

1. divide 3 by 2 to find out how many pounds of blueberries she picked each day. 3/2 is 1.5

2. multiply 1.5 by 16 to convert to ounces. 1.5x16 is 24.

3. she picked 24 ounces of blueberries each day.

Answer:

9.3

Step-by-step explanation:

last week she worked 45.6 hours. since 40 hours is the limit for normal working hours, she worked 45.6-40 = 5.6 hours overtime.

this week she worked 9.7+8.3+8+9.1+8.6 hours = 43.7 hours.

she worked therefore 43.7-40 = 3.7 hours overtime.

so, in total of the two weeks, she worked 5.6+3.7 = 9.3 hours overtime.

Answer:

he can buy 18 baseball cards

Answer:

6 gallons

Step-by-step explanation:

25÷200= 0.125

0.125×48= 6

Answer:

Heres how to solve.

Step-by-step explanation:

3 cups of sugar for every 2 teaspoons of baking soda.

So 6 cups of sugar for 4 teaspoons of baking soda.

And 9 cups of sugar for 6 teaspoons of baking soda.

Basically you just multiply by 3, 3×3=9 and 2*3=6

The number of teaspoons of baking soda Trisha needed will be 6.

It is given that Trisha uses 3 cups of sugar for every 2 teaspoon of baking soda.

We have to find out that what will be the number of teaspoons of baking soda needed for 9 cups of sugar.

If a car goes 10 km in two hours , how far will it go in one hour ?

The car will go, 10 ÷ 2 = 5 km in an hour.

As Trisha uses 3 cups of sugar for every 2 teaspoons of baking soda.

For 1 cup of sugar Trisha will have to use 2/3 teaspoons of baking soda .

For 9 cup of sugar Trisha will use ;

= (2/3) × 9 = 18 ÷ 3

= 6

So, Trisha will have to use 6 teaspoons of baking soda for 9 cups of sugar.  

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Answer:

456.9

Step-by-step explanation:

Then 1 - 3/5 = 2/5. This means that 2/5 of the frogs in that particular part of the rainforest are not poisonous. This fraction can also be expressed as 40/100 or 0.4 in decimal form.

In the given scenario, we know that 3/5 of the frogs in a particular part of the rainforest are poisonous. This means that the remaining fraction of the frogs are not poisonous.

To find this fraction, we need to subtract 3/5 from 1 (since the sum of the fractions of poisonous and non-poisonous frogs is equal to 1).

It's important to note that just because a frog is not poisonous, it doesn't mean it's safe to touch or handle them. It's always best to admire these beautiful creatures from a safe distance and leave them alone in their natural habitat.

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9514 1404 393

Answer:

  B. 8 ft

Step-by-step explanation:

The area of the rectangle is ...

  A = LW = (16 ft)(4 ft) = 64 ft²

The area of the square in terms of its side length is ...

  A = s²

For the square to have the area of the rectangle, its side length must be ...

  64 ft² = s²

  s = √(64 ft²) = 8 ft

A side of the square is 8 feet long.

Exact form: --2√5

Decimal Form: 4.47213595  

Step-by-step explanation:

The final simplification of the given expression of 2√125−3√80 in a radical form  ​ is -2√5.

An expression is a combination of some mathematical symbol such that arithmetic operator and variable such that all are constrained and create an equation.

Given the expression,

2√125−3√80​

⇒ 2√(25 × 5) - 3√(16 × 5)

⇒ 2√(5²×5) - 3√(4²×5)

⇒ 2×5√5 - 3×4√5

⇒ 10√5 - 12√5

⇒ -2√5

Hence "The final simplification of the given expression of 2√125−3√80 in a radical form  ​ is -2√5".

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Actual time is much longer than the 50-year timeframe suggested by the speaker.

How to verify the statement?

This claim is based on the assumption that the rate of pollution reduction from each factory remains constant at 80%, and the number of factories increases by 3% per annum.

To verify this claim, we can use the following formula to calculate the expected total pollution after n years:

Total pollution after n years = \(Present \: pollution \: level x (1 + 0.03)^n \times (1 - 0.8)^n\)

Here, the first factor represents the increase in pollution due to the growth in the number of factories, and the second factor represents the reduction in pollution due to the 80% reduction in pollution from each factory.

We can set the expected total pollution after n years equal to the present pollution level and solve for n:

\(Present \: pollution \: level = Present \: pollution \: level \times (1 + 0.03)^n \times (1 - 0.8)^n\)

Simplifying this equation, we get:

\(1 = 1.03^n \times 0.2^n\)

Taking the logarithm of both sides of the equation, we get,

\(n \times log(1.03) + n \times log(0.2) = 0 \\ n \times (log(1.03) + log(0.2)) = 0 \\ n = \frac{0} { (log(1.03) + log(0.2))} \\ n = 271.56\)

Therefore, according to this calculation, it would take approximately 272 years for the total annual pollution to return to its present level if the number of factories in the country increases by 3% per annum, and they all immediately reduce the amount of pollution they produce by 80%. This is much longer than the 50-year timeframe suggested by the speaker.

It is important to note that this calculation assumes that the pollution reduction from each factory remains constant at 80% and does not take into account any other factors that may affect pollution levels, such as changes in technology or regulations. Therefore, this should be considered as a rough estimate and not as an exact prediction.

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Correct question is "A speaker claimed that if the number of factories in the country increases by 3% per annum, then even if they all immediately reduced the amount of pollution they produce by 80%, the total annual pollution will be back to its present level in about 50 years. Verify the statement. (use logarithm)"

A -120 difference will be seen in the temperature within a 7 hour period

Equation

-30 x 7

Multiplying two of different signs ( - + ,  + - ) will always be negative.

Multiplying two of the same sign ( - - , + + ) will always be positive.

Answer:

one solution is the correct answer

Answer:

\(274\,\text{in}^3\)

Step-by-step explanation:

\(V=\pi r^2h=\pi(3.75)^2(6.21)\approx274\,\text{in}^3\)

Answer:

see below

Step-by-step explanation:

The answer is 1,050

123+87= 210

210 times 5= 1050

Answer:

558

Step-by-step explanation:

(123)+87 x 5

Answer:

Step-by-step explanation:

6

Our vertex has an x-coordinate of 0, so the axis of symmetry for our function is x = 0. Now, let's consider the zeros of our function. Graphically, the zeros of a function are the x-coordinates of the points where the function crosses the x-axis. This occurs where y = 0.

The derivative of the function cos(xº) in radians is y' = -sin(xπ/180)

From the question, we have the following function definition that can be used in our computation:

cos(xº)

Changing the degree into radian, we have

cos(xπ/180)

Express as a function

So, we have

y = cos(xπ/180)

When the cosine function is differentiated, we have

y' = -sin(xπ/180)

Hence, the differentiated function is y' = -sin(xπ/180)

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Answer:

Step-by-step explanation:

You can view 3x3 as 3+3+3.  3x4 is 3+3+3+3.  3x4 is also 4+4+4.  And so forth.

So, you can see how 3+3 is the same as 3x2.  

Hopefully, you can also see that 2x2 is 2+2 for the same reason.  It becomes trivial.

Answer:

2+2=4is not more then 2X4

Step-by-step explanation:

Answer:

Step-by-step explanation:

i am working on the assumption that nobody does all three of them

i got 4 because including the people that do swimming and park, the total number of people that do swimming is 22.

the same logic goes for cycling: including the people that do swimming and visit the national park, the total is 23.

so that means that find how many people do swimming and cycling, we have to add the people doing only swimming, with the people doing both swimming and park and then subtract that answer from 22 which gives you 4

Answer:

y=6x-6

Step-by-step explanation:

The slope equation is: y=mx+b

Keep in mind that m= slope and b= y-intercept

Since this problem gives us both of the things needed to complete the equation, we just need to plug it in.

m, (slope) = 6

b, (y-intercept) = -9

y= 6x-6

The art teacher can make a maximum of 24 identical kits using all the crayons and drawing paper for proper distribution.

To determine the largest number of identical kits the art teacher can make using all the crayons and drawing paper, we need to find the greatest common divisor (GCD) of the quantities.

The GCD represents the largest number that can divide all the quantities without leaving a remainder.

The GCD of the quantities of crayons can be found by considering the prime factorization:

72 = 2³ × 3²

48 = 2⁴ × 3

48 = 2⁴ × 3

48 = 2⁴ × 3

The GCD of the crayons is 2³ × 3 , which is 24.

Now, we need to find the GCD of the quantity of drawing paper:

120 = 2³ × 3 × 5

The GCD of the drawing paper is also 2³ × 3 , which is 24.

Since the GCD of both the crayons and drawing paper is 24, the art teacher can make a maximum of 24 identical kits using all the crayons and drawing paper.

Each kit would contain an equal distribution of crayons and drawing paper.

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The number of small rooms reserved is 4.

The number of large rooms reserved is 8.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

We have,

Small rooms are denoted as S.

Large rooms are denoted as L.

Now,

We will make two equations.
L = 2S _____(1)

8L + 6S = 88 ______(2)

Putting (1) in (2) we get,

8L + 6S = 88

8 x (2S) + 6S = 88

16S + 6S = 88

22S = 88

S = 88/22

S = 8/2

S = 4

Now,

Putting S = 4 in (1) we get,

L = 2 x 4

L = 8

Thus,

The number of small rooms and large rooms reserved is 4 and 8.

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