Michael is 12 years older than Lynn. The sum of the ages is 84. How old is Michael?

Answer: y=-5/2x+13

Step-by-step explanation:

Since we are given the slope, we can plug it into our equation and use the point given to find the y-intercept.

y=mx+b

y=-5/2x+b

-2=-5/2(6)+b

-2=-15+b

b=13

Now that we know the y-intercept, we can complete the equation.

y=-5/2x+13

Answer:

I think its C

Step-by-step explanation:

Explanation:

If he mowed the lawn exactly once, then 55 ≤ t ≤ 75 describes all the possible values of t. Basically t is between 55 and 75 inclusive of both endpoints.

Multiply each value by 3

55*3 = 165

75*3 = 225

That's how we end up with 165 ≤ t ≤ 225 to represent the possible span of time values where he mowed the grass three times. His fastest possible time is 165 minutes (2 hr, 45 min) and his slowest possible time is 225 minutes (3 hr, 45 min).

Answer: 8.06 Inches

The area of the circle is 28.26 ft². 3. The diameter of the circle is 8.06 inches.

Hello,

I hope you and your family are doing well!

(a) The exponential growth model is given by the equation P(t) = P0 * r^t, where P(t) is the population t years after 2010, P0 is the population in 2010 (7420), and r is the annual growth rate (2.3%).

Substituting the given values into the equation gives us:

P(t) = 7420 * 1.023^t

This is the equation that estimates the population t years after 2010.

(b) To estimate the population of the town in 2022, we can substitute t = 12 into the equation:

P(12) = 7420 * 1.023^12

Calculating this gives us:

P(12) = 7420 * 1.023^12 = 7420 * 1.291891 = 9593.45

So the estimated population of the town in 2022 is approximately 9593

Happy to help!

Step-by-step explanation:

Pick any point on the graph below for a solution:

Answer:

3/8, 5/8, 2/3

Answer:

Triangles in Geometry

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

x-y=0

straight line 45 degrees moving upwards

Answer:

Mr. Mac's fish weighed 13 pounds.

Mr Rod's fish weighed 29 pounds.

Explanation:

Let the weight of the fish caught by Mr Mac = x

The expression for Mac's fish: x

3 pounds more than twice what fish that Mr. Mac Arille caught = 2x+3

Therefore:

The expression for Rod's fish: 2x+3

The sum of the weights of the fish was 42 pounds, therefore:

We solve for x.

0. Mr. Mac's fish weighed 13 pounds.

1. Mr Rod's fish weighed 42-13 = 29 pounds.

Answer:

Its 144

Step-by-step explanation:

I did it on a test

The surface area of the square pyramid is 132 m²

For a square pyramid whose base has sides that measure b, and height h, is:

S = b*b + 4*(b*h)/2

In this case, we have:

Replacing that in the surface area equation, we get:

S = (6m*6m) + 4*(6m*8m)/2 = 132 m²

So the correct option is the first one.

If you want to learn more about surface areas:

https://brainly.com/question/6613758

#SPJ2

9514 1404 393

Answer:

  b) 24 miles per gallon

Step-by-step explanation:

The usual metric measure of vehicle fuel efficiency is liters per 100 km. Greater efficiency is indicated by a lower value.

In the US, the measure is usually miles per gallon. Greater efficiency is indicated by a higher value. Since we want the efficiency expressed in miles per gallon, we need to divide distance by fuel consumption.

  (distance)/(fuel used) = (100 km)/(10 L)

  = (100 km)/(10 L) × (1 mi)/(1.6 km) × (3.8 L)/(1 gal) = (100×3.8)/(10×1.6) mi/gal

  = 23.75 mi/gal ≈ 24 mi/gal

Answer:

volume of a cylindrical water tank = 70,650cm³

Step-by-step explanation:

volume of cylinder, V = πr²h

where π = 3.14

h = 100cm

r = ?

given is diameter = 30cm

r = d/2 = 30/2 = 15cm

substituting the values in the formula,

V = 3.14 * 15² * 100

= 3.14 * 225 * 100

= 70,650cm³                        

Answer:

How much space it would take up: 706.86 square centimeters of floor space and extend vertically to a height of 100 cm

Volume: 706,500 cm³

Step-by-step explanation:

How much space it would take up:

To determine the space occupied by a cylindrical water tank in a room, we need to consider its dimensions and the area it covers on the floor.

The diameter of the tank is given as 30 cm, which means the radius is half of that, 15 cm.

To calculate the space it occupies on the floor, we need to find the area of the circular base. The formula for the area of a circle is A = πr², where A is the area and r is the radius.

A = π(15 cm)²

A = π(225 cm²)

A ≈ 706.86 cm²

So, the circular base of the tank occupies approximately 706.86 square centimeters of floor space.

The height of the tank is given as 100 cm, which represents the vertical space it occupies in the room.

Therefore, the cylindrical water tank would take up 706.86 square centimeters of floor space and extend vertically to a height of 100 cm in the room.

Volume:

To calculate the volume of a cylindrical water tank, we can use the formula V = πr²h, where V is the volume, r is the radius, and h is the height.

First, we need to find the radius by dividing the diameter by 2:

Radius = 30 cm / 2 = 15 cm

Now we can calculate the volume:

V = π(15 cm)²(100 cm)

V = 3.14 * 225 cm² * 100 cm

V = 706,500 cm³

Therefore, the cylindrical water tank will occupy a volume of 706,500 cm³ or 706.5 liters.

Note that the parameters of the graph a and graph b are given below.

Graph A - y=2(x-1)²

See graph attached.

Graph B - y = 1/2x² + 3

Vertex: The vertex of the function is (0, 3).

Axis of symmetry: The axis of symmetry is the vertical line passing through the vertex, which is x = 0.

Y-intercept: The y-intercept is the point where the graph intersects the y-axis. It is (0, 3).

Minimum or maximum: The coefficient of x² is positive, which means the parabola opens upwards, and therefore the function has a minimum value. The minimum value is 3.

Solutions: To find the solutions or roots of the quadratic equation, we need to set y or f(x) equal to zero and solve for x.

0 = 1/2 x² + 3

Subtracting 3 from both sides, we get:

-3 = 1/2 x²

Multiplying both sides by -2, we get:

6 = -x²

Taking the square root of both sides, we get:

x = ±√(-6)

Since the square root of a negative number is not a real number, the function has no real roots.

Minimum or maximum value: The minimum value of the function is 3.

Range: The range of the function is y ≥ 3, because the function has a minimum value of 3.

Domain: The domain of the function is all real numbers, because there are no restrictions on the values of x for which the function is defined.

Stretch/Shrink/Standard: The coefficient of x^2 is positive and less than 1, which means that the graph of the function is narrower than the graph of y = x². This is an example of a standard quadratic function that has been vertically compressed by a factor of 1/2.

See graph attached.


Learn more about graphs at:

https://brainly.com/question/17267403

#SPJ1

9514 1404 393

Answer:

  -64

Step-by-step explanation:

Use your calculator to evaluate the expression. (see attached)

__

According to the order of operations, the value is found to be ...

  18(5^3 -2^7) -10

  = 18(125 -128) -10

  = 18(-3) -10

  = -54 -10

  = -64

_____

You may be familiar with some of the small powers of small integers:

  5^2 = 25, so 5^3 = 25×5 = 125

  2^3 = 8, so 2^7 = (2^3)(2^3)(2) = 8×8×2 = 64×2 = 128

Answer:

\(\displaystyle 5\)

Explanation:

All you do is deduct the people watching giraffes from the total number of people at the zoo:

\(\displaystyle \boxed{5} = -7 + 12\)

I am joyous to assist you at any time.

5 people’s are watching the otters …

12 people are watching the otters at the zoo. 7 people are watching the giraffes. How many more people are watching the otters ?

How many more people are watching the otters ?

→ At the zoo, 12 people are watching the otters & 7 people are watching the giraffes...

• So , you have to find how many people’s are watching otters more than the giraffes...

→ Then use , Subtraction to find How many more people are watching the otters..

\(12 - 7 = 5\)

• Therefore , 5 people’s are more peoples are watching the otters than the giraffes….

Answer:

0.25

Step-by-step explanation:

The number of tonnes, in 8000 ounces of the stone will be 2.11 tonnes.

Conversion means to convert the same thing into different units.

Division means the separation of something into different parts, sharing of something among different people, places, etc.

Mr. Collins ordered 8,000 oz of stone.

We know that in one tonne, there are 3785.41 ounces.

Then the number of tonnes, in 8000 ounces of the stone will be calculated by dividing 8000 by 3785.41.

⇒ 8000 / 3785.41

⇒ 2.11 tonnes

Thus, the number of tonnes, in 8000 ounces of the stone will be 2.11 tonnes.

More about the conversion link is given below.

https://brainly.com/question/9414705

#SPJ2

Answer:

side 1^2 + side 2 ^2 = hypotenuse ^ 2

18^2 + 20^2 = hypotenuse^2

324 + 400 = 724

hypotenuse^2 = 724

hypotenuse = 26.9072480941474

hypotenuse = 26.9

Step-by-step explanation:

Answer:

1. monomial

2. binomial

Step-by-step explanation:

Box 1's volume will be a monomial

Box 's volume will be a binomial

Computing the total number of counters in the class as 1,108, the mean number of counters that the 46 children have is 24.

The mean refers to the average value.

The average is the quotient of the total value divided by the number of items in the data set.

The number of boys in the class = 26

The number of girls in the class = 20

The total number of boys and girls in the class = 46

The mean number of counters that the boys have = 28

The total number of counters that the boys have = 728 (28 x 26)

The mean number of counters that the girls have =19

The total number of counters that the girls have = 380 (19 x 20)

The total number of counters that the class has = 1,108 (728 + 380)

The average or mean number of counters in the class = 24 (1,108 ÷ 46)

Learn more about the average at https://brainly.com/question/130657.

#SPJ1

Answer:

Z = 22.5, Y = 81, X = 26.7

Step-by-step explanation:

Using the lengths you do know compare them to the copy, the only two lengths available that are for the same side length are 33 and 22, divide them together and you get 1.5. Thats the scale factor. Everything else you can figure out by multiplying or dividing by this scale factor.

\(Z = (15)(1.5) = 22.5\\Y = (54)(1.5) = 81\\X = (40)/(1.5) = 26.7\)

a) The inequality for the expression 2z + 9 is 2z + 9 > 13.

b) The inequality for the expression 3(z - 4) is 3z - 12 > -6.

c) The inequality for the expression 4 + 2z is 4 + 2z > 8.

d) The inequality for the expression 5(3z - 2) is 15z - 10 > 20.

a) To write an inequality for the expression 2z + 9, we can multiply the given inequality z > 2 by 2 and then add 9 to both sides of the inequality:

2z > 2 * 2

2z > 4

Adding 9 to both sides:

2z + 9 > 4 + 9

2z + 9 > 13

Therefore, the inequality for the expression 2z + 9 is 2z + 9 > 13.

b) For the expression 3(z - 4), we can distribute the 3 inside the parentheses:

3z - 3 * 4

3z - 12

Since we are given that z > 2, we can substitute z > 2 into the expression:

3z - 12 > 3 * 2 - 12

3z - 12 > 6 - 12

3z - 12 > -6

Therefore, the inequality for the expression 3(z - 4) is 3z - 12 > -6.

c) The expression 4 + 2z does not change with the given inequality z > 2. We can simply rewrite the expression:

4 + 2z > 4 + 2 * 2

4 + 2z > 4 + 4

4 + 2z > 8

Therefore, the inequality for the expression 4 + 2z is 4 + 2z > 8.

d) Similar to the previous expressions, we can distribute the 5 in the expression 5(3z - 2):

5 * 3z - 5 * 2

15z - 10

Considering the given inequality z > 2, we can substitute z > 2 into the expression:

15z - 10 > 15 * 2 - 10

15z - 10 > 30 - 10

15z - 10 > 20

Therefore, the inequality for the expression 5(3z - 2) is 15z - 10 > 20.

for such more question on inequality

https://brainly.com/question/17448505

#SPJ8

The standard deviation of the sample is 0.63

What is standard deviation?

A random variable, sample, statistical population, data set, or probability distribution's standard deviation is equal to the square root of its variance.

To find the standard deviation of the sample, we need to first find the mean of the distribution. The mean of a distribution is given by the expected value of the random variable, which can be calculated as follows:

       \(E[X] = \int\limits {xf(x)dx}\)

Substituting the given pdf for f(x), we get:

     \(E[X] = \int\limits {x(x2 + Źosxs1)dx}\)

Evaluating the integral, we get:

   \(E[X] = (x3/3) + (Źosxs2/2) |0\\\\ E[X] = (1/3) + (0/2)\\\\ E[X] = 1/3\)

Next, we need to find the variance of the distribution. The variance of a distribution is given by the expected value of the squared deviation of the random variable from its mean, which can be calculated as follows:

\(Var[X] = E[(X - E[X])2]\)

Substituting the value of E[X] that we just found, we get:

Var[X] = E[(X - (1/3))2]

Var[X] = ∫((x - (1/3))2)(x2 + Źosxs1)dx

Evaluating the integral, we get:

Var[X] = ((x - (1/3))2)(x2 + Źosxs1) |0

Var[X] = ((1 - (1/3))2)(1 + 0) - ((0 - (1/3))2)(0 + 0)

Var[X] = (4/9)(1) - (1/9)(0)

Var[X] = 4/9

Finally, the standard deviation of the distribution is the square root of the variance, which is:

\(Std\ Dev[X] = \sqrt{Var[X]}\\\\ Std\ Dev[X] = \sqrt{(4/9) } \\\\Std\ Dev[X] = 0.63\)

Rounding off to the second decimal place, the standard deviation of the sample is 0.63.

Hence, The standard deviation of the sample is 0.63

To know more about standard deviation visit,

https://brainly.com/question/475676

#SPJ4

Answer:

Step-by-step explanation:

If we are looking for the ratio of the area of the inner square to the area of the outer square, that means that we need the areas of each of these squares, and we need to find the areas without any numbers. But that's ok; the answer they want is not a number answer. The answer will have a's and b's in it instead of numbers.

First the area of the inner square. Here we go:

Look at the triangle in the lower left corner of this coordinate plane. It is a right triangle. The height of it is b. That's because the height is a "y" thing and the y-coordinates of each of those sets of coordinates is b and 0. The height is then b - 0 = b.

The length of the base is a - b. That's because the length is an "x" thing and the x-coordinates of each of those sets of coordinates is (a - b) and 0. The length is then a - b - 0 = a - b.

Now we need the length of the hypotenuse which also serves as one of the sides of the inner square. Using Pythagorean's Theorem, we can find the length of the hypotenuse, which I will label as "?":

\(?^2=b^2+(a-b)^2\) and

\(?^2=b^2+a^2-2ab+b^2\) and

\(?^2=a^2-2ab+2b^2\) so

?, the length of the hypotenuse, is

\(?=\sqrt{a^2-2ab+2b^2}\) and now we can use that to find the area of the inner square. The formula for a square's area is

\(A=s^2\) so

\(A=(\sqrt{a^_2}-2ab+2b^2})^2\) which gives us finally:

\(A=a^2-2ab+2b^2\) **

Now for the outer square. Those blue triangles you see are all congruent. We can use the side lengths for the triangles we found above to find the length of a side of the outer square. One side of the outer square is made up of one base length of these triangles and one height. We found the base length to be (a - b) and the height to be b; therefore, the length of one side of the outer square is b + (a - b) which is just "a". That's is, just a length of "a". The area is found by multiplying this side length by itself, so the area of the outer square is

A = a²

The ratio of the area of the inner to the outer is:

\(\frac{A_i}{A_o}:\frac{a^2-2ab+2b^2}{a^2}\) and that does not reduce.

Answer:

A

Step-by-step explanation:

Edmentum

Answer:

17.5?

Step-by-step explanation:

The numerical value of x in angle ABD is 9 as angle ABC is divided into two equal halves.

An angle bisector divided an angle into two equal halves.

From the diagram:

Line BD divides angle ABC into two equal halves.

Angle ABD = ( 3x - 7 ) degrees

Angle DBC = 20 degrees

Since angle ABD and DBC are equal haves;

Angle ABD = Angle DBC

Plug in the values:

( 3x - 7 ) = 20

Solve for x:

3x - 7 = 20

Add 7 to both sides:

3x - 7 + 7 = 20 + 7

3x = 27

x = 27/3

x = 9

Therefore, the value of x is 9.

Option A)9 is the correct answer.

Learn more about angle bisector here: brainly.com/question/28565813

#SPJ1

Hello there. To solve this question, we'll need to remember some properties about trigonometry.

Let's start by drawing the situation:

Since we don't know Jane's height, we don't need to consider the point of view starting by her eye height. In this case, we can solve directly for the height of the monument.

For this, we'll use the tangent. This trigonometric function relates the opposite side to an angle to its adjacent side by the following ratio:

Using opposite side as h (for height), adjacent side is the distance between Jane and the monument, 1000 and alpha equals to the angle 29º, we have:

tan(29º) = h/1000

Multiply both sides of the equation by 1000

h = 1000tan(29º)

Using a calculator, we have that tan(29º) is approximately equal to 0.5543

Hence, we have that

h approx. 55.43 meters.

Answer: 8>a

Step-by-step explanation:

If 8 is greater than a, then this symbol > would be pointing at the 8. Think of it as a hungry mouth. It would rather have more food then less food, which is why is points at the 8.

The graph shows that the total fare changes by $3 and the fare for 6 kilometers is $22

We can see that the line graph is the method that we could be able to use to present information in two axis. There is a vertical axis and there is a horizontal axis.

In order to obtain the fare that could be charged per kilometers then we have to use the formula for the slope of the graph as;

m = \(y_{2} - y_{1} /x_{2} - x_{1}\)

We would now have;

m = 16 - 4/ 4 - 0

m = 3

Thus the fare is seen to change by $3 each time we board.

Learn more about slope of graph:https://brainly.com/question/28756431

#SPJ1