What Is the term -3x and 5x combined to?

Mean age: 16.1 years, Sample variance: 50.47 square years and Sample standard deviation: 7.10 years for the given problem.

To estimate the mean age, we need to find the midpoint of each age range and multiply it by the number of individuals in that range. Then we add up these products and divide by the total number of individuals:

Mean age = [(1+10)/2 x 35 + (11+20)/2 x 22 + (21+30)/2 x 20 + 35.5 x 7] / 84

= (5.5 x 35 + 15.5 x 22 + 25.5 x 20 + 35.5 x 7) / 84

= 16.1

Therefore, the estimated mean age of this extended family group is 16.1 years.

To calculate the sample variance, we need to find the deviation of each age from the mean, square each deviation, and add up these squared deviations. Then we divide this sum by the total number of individuals minus one:

s2 = [(1-16.1)2 x 35 + (11-16.1)2 x 22 + (21-16.1)2 x 20 + (35.5-16.1)2 x 7] / (84-1)

= (2254.05 + 537.08 + 220.89 + 253.68) / 83

= 50.47

Therefore, the estimated sample variance is 50.47 square years.

We simply take the square root of the sample variance to calculate the sample standard deviation:

s = \(\sqrt{s2}\)

= s\(\sqrt{50.47}\)

= 7.10

Therefore, the estimated sample standard deviation is 7.10 years.

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Answer:

Multiply by 5

Step-by-step explanation:

30 people in class and the recipe makes 6 bowls. 30/6= 5, so you need to multiply the recipe by 5 to make enough for each person to have one bowl of stew.

7.5 tablespoons of oil

5 small onions

10 cloves of garlic

7.5 lbs of caribou

12.5 cups of broth

12.5 cups of diced celery

12.5 cups of diced carrots

15 potatoes

2.5 teaspoons of salt

5 dashes of pepper

Answer:

It can't be simplified. 4/35 IS simplest form.

The first five terms of the sequence with a = 3 and r = -2 are: 3, -6, 12, -24, 48.

The general formula for a geometric sequence is given by:

an = a * r^(n-1)

where "a" is the first term, "r" is the common ratio, and "n" is the number of the term we want to find.

In this case, we have:

a = 3

r = -2

So the first term is 3, and the common ratio is -2. We can use the formula above to find the first five terms of the sequence:

a1 = 3

a2 = 3 * (-2)^(2-1) = -6

a3 = 3 * (-2)^(3-1) = 12

a4 = 3 * (-2)^(4-1) = -24

a5 = 3 * (-2)^(5-1) = 48

Therefore, the first five terms of the geometric sequence with a = 3 and r = -2 are: 3, -6, 12, -24, 48.

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Answer:

The length of AB is 18

Step-by-step explanation:

Do the pygotham theorem

24^2 + 7^2 = 625

Square root the answer

\(\sqrt{625}\) = 25

Line BO equals 7 because CO is 7 and they are both radiuses

Subtract the answer to the length BO

25 - 7 = 18

18 is the length of AB bro

When the domain is substituted, the Range of the function will be

7 ≤ y < ∞

The range of a function is the the spread of minimum value of the function to maximum value. We can find the range by substituting different domains into the function.

Given a function  f(x) = |x| + 7

This |x| show that it is a modulus. That is, the domain will always be positive numerals.

The minimum domain = 0, so the minimum f(x) = 0 + 7 = 7

The maximum domain = ∞, so the maximum f(x) = ∞ + 7 = ∞

y = f(x)

Therefore, the range of of the function f(x) = |x| + 7 will be 7 ≤ y < ∞

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Answer:

8 pigs

Step-by-step explanation:

Since every animal has only 1 head, a total of 26 heads suggests that there are 26 animals in total.

Suppose all animals are chickens.

Total no. of feet = 26 chickens × 2 feet

                           = 52 feet

Difference in total no. of feet = 68 feet - 52 feet

                                                = 16 feet

Difference in no. of feet each animal has

= 4 feet (a pig) - 2 feet (a chicken)

= 2 feet

∴ No. of pigs = 16 feet ÷ 2 feet

                      = 8 pigs

Answer:

C and D

Step-by-step explanation:

So basically when u square -5 or +5, u get 25 either way

And since the square root of x is greater than or equal to 25, u can use both of them for answers.

Answer:

10i

Step-by-step explanation:

We can separate \(\sqrt{-100}\) into \(\sqrt{100*-1}\). This equals \(10*\sqrt{-1}\), and since \(\sqrt{-1}=i\), it is \(10i\).

Answer:0 + 10i

Step-by-step explanation:

Answer:

150

Step-by-step explanation:

Collected bills: 18 * 10= 180

1/6 of 180 = 30

180-30=150

Answer:

15 ten dollar bills, 150 dollars

Step-by-step explanation:

1/6 of 18 is 3, so he gave 3 bills to the theater and kept the other 15 for himself

The total amount that the Bells will pay for their house would be $313, 680.

The cost that would be interest is $193, 680

The amount of the first payment going to mortgages is $165. 24

Find the down payment :

Down payment = House price - Mortgage amount = $120,000 - $90,000 = $30,000

Then the points paid at closing :

= $ 90,000 x 0. 02 = $1,800

Total amount paid = Total mortgage payments + Down payment + Points cost

= 281, 880 + 30, 000 + 1, 800

= $ 313, 680

The total that is interest is:

Total interest paid = Total interest paid through monthly payments + Points cost

Total interest paid = $ 191, 880 + $ 1, 800 = $193, 680

The amount of the first payment going to principal is:

Principal portion of first payment = 90, 000 - 89, 834.76 = $165. 24

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The distance you can see along the surface of the earth from the top of a tower of height h above the surface is approximately s = v(2hR), where R is the radius of the earth.

When you are at the top of a tower height h above the surface of the earth, you can see a certain distance along the surface. This distance can be approximated by the formula s = v(2hR), where R is the radius of the earth.

To understand why this formula works, imagine drawing a triangle with the tower, the point where you are looking, and the point on the surface of the earth directly below your line of sight. This forms a right triangle, where the height is h, the hypotenuse is the distance you can see (s), and the base is the radius of the earth (R).

Using the Pythagorean theorem, we can solve for s:

Taking the square root of both sides, we get:

Since R is much larger than h, we can approximate s as:

Expanding this expression using the binomial theorem and dropping the higher-order terms, we get:

Therefore, the distance you can see along the surface of the earth from the top of a tower of height h above the surface is approximately s = v(2hR), where R is the radius of the earth.

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The point that is 1/3rd of the distance from (-4.5,0) to (0,9) is (-3,3).We use a formula similar to the midpoint formula for finding the point.

We have been given two points (-4.5,0) and (0,9), we have to find the point is on the line formed by these two points and is 1/3rd away. We don't need to find the distance between these two points to find the asked point. We have to use a formula that is similar to finding the midpoint of a line. For two points (a,b) and (x,y) the midpoint is (\(\frac{a+x}{2} ,\frac{b+y}{2}\)).We used equal parts of the two points to find the midpoint, for 1/3rd we will be using uneven parts of the two points.

\(x_{1} =\frac{2}{3} (-4.5)+\frac{1}{3} (0)=-3\)

\(y_{1} =\frac{2}{3} (0)+\frac{1}{3} (9)=3\)

Therefore the point that lies 1/3rd of the distance from (-4.5,0) and (0,9) is (-3,3).

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Answer:

2cm

Step-by-step explanation: Because it doesn’t tell you it, you have to subtratc 10-8. And that gets you 2

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Therefore , the solution of the given problem of equation comes out to be factor is (5b)(-5b+3).

A formula for connecting two statements using the equal sign (=) to denote equivalence is known as a mathematical equation. A mathematical equation in algebra is a statement that proves the equality of two mathematical expressions. For instance, the formula 3x + 5 = 14 places an equal sign between the variables 3x + 5 and 14. The mathematical relationship between the two sentences on either side of a letter is established. Most of the time, the symbol serves as both the one and only variable. for instance, 2x – 4 = 2.

Here,

the two numbers' primary factors are as follows:

-25\(b^{2}\) + 15b

Common prime factors can be multiplied to determine the GCF:

=> -25\(b^{2}\)  = -(5)(5) * \(b^{2}\)

=> 15b = (5)(3)b

The expression can be factored in the following fashion because the GCF is 5b:

=> -(5)(5) * \(b^{2}\) +  (5)(3)b

=> (5b)(-5b+3)

Therefore , the solution of the given problem of equation comes out to be factor is (5b)(-5b+3).

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Answer:

D. x=6

Step-by-step explanation:

-3x + 5= -2x -1

more variables to left hand side and change its sign

-3x+2x+5=-1

move constant to right hand side and change its sign

-3x+2x=-1-5

collect like terms

-x=-1-5

calculate the difference

-x=-6

change the signs on both sides of the equation

x=6

Work Shown:

21/35 = (7*3)/(7*5) = 3/5

Answer:

D

Step-by-step explanation:

The greatest common factor of 12 and 24 is 12. The only option which accounts for this is D.

Volume of the cylinder =  6838.92 cubic inches

We have to given that;

Sam needs to fill a cylindrical container with punch.

And, The container has a radius of 11 inches and a height of 18 inches.

Since, To determine the amount of cat litter the cylinder can hold, we need to calculate the volume of the cylinder.

Volume of a cylinder = πr²h

Where,

r=radius

h= height

Then,

π=22/7 or 3.14 (constant value)

r=11 inches

h=18 inches

Volume of a cylinder is,

= 3.14 × (11)² × 18

= 6838.92 cubic inches

Hence, Volume of the cylinder =  6838.92 cubic inches

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Answer:

  Patty, Karla, Cathy

Step-by-step explanation:

The scoring percentage of goals attempted can be computed by dividing goals made by those attempted, then multiplying the result by 100%.

__

Cathy's rate is ...

  27/54 × 100% = 50%

Karla's rate is ...

  18/45 × 100% = 40%

Patty's rate is ...

  given as 34%

__

By least to greatest scoring rate, the athletes are ...

  Patty (34%), Karla (40%), Cathy (50%)

Answer:

7x-y=-30

Step-by-step explanation:

The slope of any parallel equation has to have the same slope, so our equation will be in the format of y=7x+b

No you have to use this to solve for b

2 = -4*7+b

2=-28+b

30 = b

So our equation would be y = 7x+30

Now to convert into standard form we would have to put it intto the format of Ax + By = C

so -7x+y = 30

7x - y = -30

Total earnings < Ticket cost,  this inequality represents this situation.

The inequality, A declaration of relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to. Equations and questions can both be used to formulate and answer inequality problems.

Write two values   being compared in the problem in step one. Decide the first value is greater or less than the second value in step two.In step third Insert  inequalities symbol between the first and second values if the first value is greater than the second.

We calculate who earned enough money to buy a ticket,than need to calculate the total amount earned by each friend.

For  the total amount earned by each friend by multiplying the number of hours worked by hourly rate,

In Friend 1; 5 hours x $9.10 per hour = $45.50

In  Friend 2; 4 hours x $9.10 per hour = $36.40

In Friend 3; 7 hours x $9.10 per hour = $63.70

In Friend 4; 3 hours x $9.10 per hour = $27.30

In Friend 5; 6 hours x $9.10 per hour = $54.60

If each friend earned enough money to buy a ticket, than need to compare their total earnings to the cost of a ticket =$75.99. That is, Total earnings ≥ Ticket cost

Now ,substitute their total earnings for each friend,

In,Friend 1; $45.50 ≥ $75.99 that is Not enough money

In Friend 2; $36.40 ≥ $75.99 that is Not enough money

In Friend 3; $63.70 ≥ $75.99 that is Not enough money

In Friend 4; $27.30 ≥ $75.99 that is Not enough money

In Friend 5; $54.60 ≥ $75.99 that is Not enough money

Nobody   of  friends earned enough money to buy a ticket,

therefore ,Total earnings < Ticket cost.

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The number line where we plotted 1 1/4 and 5/2 is added as an attachment

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

-1 1/4 and 5/2

To start with, we convert both numbers to the same form

i.e. decimal or fraction

When converted to fractions, we have

-5/4 and 5/2

Rewrite the denominators of the fractions

So, we have

-5/4 and 10/4

This means that we can plot -5/4 at -5 and 10/4 at point 10 where the difference in each interval is 1/4

Using the above as a guide, we have the following:

The number line is attached

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There are 7 days in a week.

1/2 hour x 7 days = 3 1/2 hours per week.

3 1/2 hours per week x 4 weeks = 14 hours

He read for a total of 14 hours

Answer:

14 hours

Step-by-step explanation:

half hour = 30 minutes

1 week = 7 days

30(minutes) x 7(days) = 210 minutes

210(minutes) x 4(weeks) = 840 minutes

Now we know how much time Danny has read (840 minutes), but we need to know what that is in hours.

840 minutes = how long Danny has read in minutes

60 minutes = hour

840(minutes) ÷ 60(minutes) = 14(hours)

Answer:

2. c) 1050 mm³

3. c) 8 yards.

Step-by-step explanation:

Given the following data;

Length = 25mm

Width = 7 mm

Height = 6 mm

To find the volume of the rectangular prism;

Volume of rectangular prism = base area * height

First of all, we would determine the base area;

Base area = length * width

Base area = 25 * 7

Base area = 175 mm²

Next, we find the volume;

Volume of rectangular prism = 175 * 6

Volume of rectangular prism = 1050 mm³

Question 2.

Given the following data;

Length = 9 yards

Width = 7.5 yards

Volume = 540 cubic yards

To find the height of the rectangular prism, x;

Volume of rectangular prism = length * width * height

540 = 9 * 7.5 * x

540 = 67.5x

x = 540/67.5

Height, x = 8 yards

Answer:

x = 4

m<AXC = 150

Step-by-step explanation:

m<1 + m<2 = m<AXC

102 + 10x + 8 = 6(6x + 1)

10x + 110 = 36x + 6

26x = 104

x = 4

m<AXC = 6(6x + 1)

m<AXC = 6(24 + 1)

m<AXC = 150

Answer:

a)Range= 25.9

b)Variance =49.344

c)Standard deviation=7.0245

Step-by-step explanation:

Data : 28.2 49.2 30.9 28.8 28.0 25.9 34.0 29.0 23.8 30.1

Maximum Value : 49.4

Minimum Value : 23.5  

Range= Maximum - Minimum

Range= 49.4 -23.5 = 25.9

(b)

\(Mean=\bar{x}=\frac{\sum x}{n}=\frac{309.2}{10}=30.92\\\\Variance=s^{2}=\frac{\sum \left ( x-\bar{x} \right )^{2}}{n-1}=49.344\)

(c) Sample standard deviation:

\(s=\sqrt{\frac{\sum \left ( x-\bar{x} \right )^{2}}{n-1}}=7.0245\)

d)s2 using the shortcut method.

            X          \(X^2\)

          28.6 817.96

          49.4 2440.36

          30.3 918.09

          28.2 795.24

         28.9 835.21

         26.4 696.96

        33.8 1142.44

         29.9 894.01

         23.5 552.25

          30.2 912.04

Total   309.2 10004.56

\(s=\sqrt{\frac{\sum x^{2}_{i}-\frac{\left ( \sum x_{i} \right )^{2}}{n}}{n-1}}\\s=\frac{10004.56-\frac{309.2^{2}}{10}}{9}\\s=7.0245\)

Answer:

A. True

Step-by-step explanation:

Answer: B. False.

Step-by-step explanation:

Hope this helps!