if martha can rake the yard in 4 hours and her brother can rake the yard in 8 hours, how long does it take them to do it together?

Answer:

45 feet

Step-by-step explanation:

64-19=45

Answer:

83

Step-by-step explanation:

if it rose you need to add 64+19 correct me if im wrong

Answer:

20.5 hours

Step-by-step explanation:

Answer:

20.5 hours

Step-by-step explanation:

200+49x=1204.50

49x= 100.4

x= 20.5 hours

\(\longrightarrow\)Let us write all expression in factorised form .

\(\leadsto\) Common factors are 2,x,y,z and their product will give us highest common factor

\(\implies \sf 2\times x\times y \times z\)

\(\implies \sf 2xyz\)

The solution to the system of equations is:

X = -171, Y = -531, and Z = 363.

To solve the system of equations:

2X + 4Y + 2Z = 144 (Equation 1)

0.5X + 0.25Y = 60 (Equation 2)

1.5X + 0.5Y + Z = 36 (Equation 3)

We can use row operations to simplify and solve the system.

Let's start with Equation 2. Multiply both sides of Equation 2 by 4 to eliminate decimals:

2X + Y = 240 (Equation 4)

Now, let's solve Equations 1 and 4 using row operations. Multiply Equation 4 by -2 and add it to Equation 1:

-4X - 2Y = -480 (Equation 5)

2X + 4Y + 2Z = 144 (Equation 1)

   2Y + 2Z = -336  (Equation 6)

Next, let's solve Equations 3 and 6 using row operations. Multiply Equation 6 by -3 and add it to Equation 3:

-3Y - 3Z = 1008 (Equation 7)

1.5X + 0.5Y + Z = 36 (Equation 3)

1.5X - 2.5Z = -972 (Equation 8)

We now have a simplified system of equations:

2Y + 2Z = -336 (Equation 6)

1.5X - 2.5Z = -972 (Equation 8)

-3Y - 3Z = 1008 (Equation 7)

Now, we can solve this system by using additional row operations.

Multiply Equation 6 by 1.5 and add it to Equation 8:

-4Z = -1452

Solving for Z, we get Z = 363.

Substituting the value of Z back into Equation 6, we can solve for Y:

2Y + 2(363) = -336

2Y = -1062

Y = -531.

Finally, substituting the values of Y and Z into Equation 7, we can solve for X:

-3(-531) - 3(363) = 1008

X = -171.

Therefore, the solution to the system of equations is:

X = -171, Y = -531, and Z = 363.

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3/10 is the chance that a number selected at random from first 40 natural numbers is a multiple of either 4 or 14.

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we might discuss the likelihood or likelihood of several outcomes. Statistics is the study of occurrences that follow a probability distribution.

Given: first 40 natural numbers

To find: the probability of getting a multiple of either 4 or 14

According to the question, n(S) = 40.

Hence the probability of getting a multiple of either 4 or 14 = probability of getting a multiple of 4 or probability of getting a multiple of 14:

\(\frac{10}{40} + \frac{2}{40} = \frac{12}{40} = \frac{3}{10}\) is the required probability.

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Answer:

x = 90

Step-by-step explanation:

The other unlabled angle in the triangle forms a 180 degree angle with 130 degrees (because they make a straight line). So it can be found by subtracting 130 from 180, which equals 50.

The sum of all the angles in a triangle is 180.

180 - 50 - 40 = x

90 = x

Hello! My name is Galaxy and I'll be helping you solve this problem. We can split this problem into two steps. Them being Theory and Solving.

I'll go ahead and start with the Theory.

We can start off by looking at the image you've provided, we can see a triangle that has 2 angles given of a triangle, and an exterior angle of the triangle.

This being said, we can apply the Exterior Angle Theorem.

We can now begin to solve for the missing angle.

We can begin to solve by using our given angles to find the third angle.

According to the Exterior Angle Theorem, we know that the unknown angle along with the \(40\)° angle must add up to the \(130\)° angle.

Therefore, we can solve for \(x\),

\(x+40=130\\x=130-40\\x=90\)

After this, we know that angle \(x\) is equal to 90°.

Cheers,

Galaxy

Combination of red and yellow paint that follows the ratio of 3 parts yellow for every 2 parts red will make the shade of orange Lin needs.

Red  Yellow  

2   3

4   6

6   9

8   12

The formula for this specific shade of orange paint is 3 parts yellow for every 2 parts red. To calculate the amounts of red and yellow paint that can be used for different combinations we can use the following equation:

Yellow = 2 x Red/3

For the first combination of 2 parts red and 3 parts yellow, the equation can be written as:

Yellow = (2 x 2)/3

Simplified, that is 2/3, or 3 parts yellow.

For the second combination of 4 parts red and 6 parts yellow, the equation can be written as:

Yellow = (2 x 4)/3

Simplified, that is 4/3, or 6 parts yellow.

For the third combination of 6 parts red and 9 parts yellow, the equation can be written as:

Yellow = (2 x 6)/3

Simplified, that is 8/3, or 9 parts yellow.

For the fourth combination of 8 parts red and 12 parts yellow, the equation can be written as:

Yellow = (2 x 8)/3

Simplified, that is 16/3, or 12 parts yellow.

Therefore, any combination of red and yellow paint that follows the ratio of 3 parts yellow for every 2 parts red will make the shade of orange Lin needs.

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Answer:

- 7/1 is the simplified fraction for 14/2.

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

do 14/2 in a calculator! (dividing)

Answer:

3.9

Step-by-step explanation:

pythagorean theorem states:

\(a^{2} +b^{2} =c^{2}\)

We know that a is the height of the triangle, 2.

We also know that b is the base of the triangle, 3.

So, solve for c:

2²+3²=c²

simplify

4+9=c²

15=c²

take the square root of both sides

c=3.9

So, the spider and the fly are 3.9 ft apart from each other

Hope this helps :)

Answer:

3.6 feet

Step-by-step explanation:

The Pythagorean theorem states that a^2+b^2=c^2, where c is the hypotenuse, or longest side of the triangle opposite to the right angle, and a and b are the two legs of the triangle (the other two sides.)

In the question, sides a and b are given as 2ft and 3ft long. Plugging 2 and 3 into the equation, we will get that 2^2+3^2=c^2. 2 x 2 = 4 and 3 x 3 = 9, so 4 + 9 = c^2, or, c^2 = 13.

However, this is still c^2, not c, so we must take the square root of both sides. This is because the equation is now essentially saying that c x c = 13, so if we find a number that when multiplied by itself equals 13, that number will be c. to do this, we must take the square root of 13. This will give us an irrational number- approximately 3.605551275. The question asks to round it to the nearest tenth though, so this will simply become 3.6.

In the context of this question, it means that the spider and the fly are 3.6ft apart.

Answer:

666

Step-by-step explanation:

The shortest routes between each pair of nodes are:
- Fruit - Hay: Fruit - Shade - Grass - Hay or Fruit - Shade - Barn - Hay (tied for shortest route)
- Grass - Pond: direct route with a distance of 190

To determine the shortest route between a pair of nodes, we need to consider all possible routes and compare their distances.

In this case, we have five pairs of nodes to consider: Fruit - Hay, Grass - Pond, Fruit - Shade, Barn - Pond, and Fruit - Pond.

Starting with Fruit-Hay, we don't have any direct distance given between these two nodes. However, we can find a route that connects them by going through other nodes.

One possible route is Fruit - Shade - Grass - Hay, which has a total distance of 165 + 95 + 60 = 320.

Another possible route is Fruit - Shade - Barn - Hay, which has a total distance of 165 + 35 + 120 = 320.

Therefore, both routes have the same distance and are tied for the shortest route between Fruit and Hay.

Moving on to Grass-Pond, we have a direct distance of 190 between these two nodes.

Therefore, this is the shortest route between them.

For Fruit-Shade, we already considered one possible route when looking at Fruit-Hay.

However, there is also another route that connects Fruit and Shade directly, which has a distance of 165.

Therefore, this is the shortest route between Fruit and Shade.

Looking at Barn-Pond, we don't have a direct distance given. We can find a route that connects them by going through other nodes.

One possible route is Barn - Hay - Grass - Pond, which has a total distance of 120 + 60 + 190 = 370. Another possible route is Barn - Shade - Fruit - Pond, which has a total distance of 35 + 165 + 300 = 500.

Therefore, the shortest route between Barn and Pond is Barn - Hay - Grass - Pond.

Finally, we already considered Fruit-Pond when looking at other pairs of nodes. The shortest route between them is direct, with a distance of 300.

In summary, the shortest routes between each pair of nodes are:

- Fruit - Hay: Fruit - Shade - Grass - Hay or Fruit - Shade - Barn - Hay (tied for shortest route)
- Grass - Pond: direct route with a distance of 190
- Fruit - Shade: direct route with a distance of 165
- Barn - Pond: Barn - Hay - Grass - Pond
- Fruit - Pond: direct route with a distance of 300

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The population size of mantis shrimp will be approximately 266 individuals after 5 years.

The intrinsic rate of increase is an essential concept in population biology. It is the rate at which a population is growing at a particular moment in time. The population size after a particular period can be calculated using the intrinsic rate of increase with the help of this formula:

Nt = N0e^(rt)

where Nt is the future population size, N0 is the initial population size, r is the intrinsic rate of increase, and t is the time in years.

The population size of mantis shrimp is 475 individuals and the intrinsic rate of increase is -0.10.

We can calculate the population size after 5 years using the above formula as follows:

Nt = N0e^(rt)

Nt = 475 * e^(-0.10 * 5)

Nt = 475 * e^(-0.50)

Nt ≈ 266

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1

Function notation is a helpful way to represent a relationship between x and y.

Function Notation

Function notation is often expressed as f(x) = x. This is said as "f of x equals x." The "f(x)" presents the y-value. While f(x) is the most common, any letter can be used. In this case, h is used instead of f. In function notation, you have h(x) set equal to some function. The variable inside the parentheses is the independent variable of the function.

Additionally, if a constant is in the parentheses, then the function should be solved for that constant. This means to find h(2), we should plug 2 in for x and solve.

Solving the Function

To solve this, we need to plug 2 in.

Then, simplify and solve.

This means that given the function, h(2) is equal to 1.

Answer: Look below

Step-by-step explanation:

Chase and Simon (1973) conducted a study on the memory of chess novices and experts for positions of chess pieces on a chessboard. They found that although experts generally have a better memory for chess positions than novices, novices performed equally or even better than experts when asked to recall random arrangements of chess pieces on the chessboard, even if the arrangements couldn't occur in a real game of chess.

One possible explanation for this phenomenon is that experts rely heavily on their knowledge of typical chess positions and patterns to remember the positions of the pieces. However, when the pieces are arranged randomly, these patterns are disrupted, and experts may struggle to apply their existing knowledge effectively. On the other hand, novices may not have developed strong patterns or strategies yet, so they approach the task with a more flexible mindset and are less affected by the random arrangement. They may use more general memory strategies, such as chunking or grouping the pieces together, which can be useful for recalling random arrangements.
In summary, novices may perform as well as experts when the pieces are arranged randomly because they rely less on established patterns and can use more general memory strategies to recall the positions.

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Solution:

Note that:

Let's substitute the values into the equation and find the measure of AC.

Answer:

∠ QPR = 56°

Step-by-step explanation:

Δ RST is isosceles ( 2 congruent sides ) , then base angles are congruent

∠ SRT = \(\frac{180-44}{2}\) = \(\frac{136}{2}\) = 68°

∠ PRQ and ∠ SRT are vertically opposite angles and are congruent , so

∠ PRQ = 68°

Δ PRQ is isosceles ( 2 congruent sides ), then base angles are congruent , so

∠ QPR = \(\frac{180-68}{2}\) = \(\frac{112}{2}\) = 56°

=====================================================

Explanation:

Triangle TRS is isosceles due to the sides TR and TS being congruent.

Let x be the measure of angle R of triangle TRS. It's also the measure of angle S. The base angles of any isosceles triangle are the same.

Add up the three angles of triangle TRS. Set the sum equal to 180. Solve for x.

T+R+S = 180

44+x+x = 180

44+2x = 180

2x = 180-44

2x = 136

x = 136/2

x = 68

This means angle TRS is 68 degrees.

Subsequently, it also means angle QRP is 68 degrees as well. These two angles are congruent vertical angles.

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

Now focus on triangle PQR. This triangle is also isosceles.

We have the following interior angles

So,

P+Q+R = 180

y+y+68 = 180

2y+68 = 180

2y = 180-68

2y = 112

y = 112/2

y = 56 is the measure of angle QPR

Answer:

\(a_{n}\) = 2n - 3

Step-by-step explanation:

the nth term of an arithmetic sequence is

\(a_{n}\) = a₁ + d(n - 1)

where a₁ is the first term and d the common difference

given a₁ = - 1 and a₅ = 7 , then

a₁ + 4d = 7 , that is

- 1 + 4d = 7 ( add 1 to both sides )

4d = 8 ( divide both sides by 4 )

d = 2

then

\(a_{n}\) = - 1 + 2(n - 1) = - 1 + 2n - 2 = 2n - 3

\(a_{n}\) = 2n - 3

Answer: When combining like terms, add or subtract the coefficients. Keep the exponents as they are.

Step-by-step explanation:

You can combine 2x^2 + 3x^2 to get 5x^2. If x =3, 3^2=9 So 2(3)^2 is 18 and 3(3)^2 is 27. 18+27=45 And 5(3)^2= 45. Same result!

You can not combine 2x^2 and 2x^3. If the value of x is 3, 2(3)^2 this term works out to =18 and 2(3)^3 =54

If you add the exponents x^5 becomes 2(3)^5 or 2×243=486. Vastly different values! Don't add exponents unless you are multiplying terms.

Yes, when combining like terms with exponents, you add the exponents only if the terms have the same base.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

When combining like terms with exponents, you add the exponents only if the terms have the same base.

For example,

3x² + 9x²

= (3 + 9)x²

= 12x²

And,

2² x 2³

= \(2^{2 + 3}\)

= \(2^5\)

Thus,

Yes, we add the exponents.

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The manufacturer estimates that about 1% of the light bulbs are defective. We can solve for the probability of defective bulbs using the binomial probability distribution formula. A package of 10 lightbulbs is taken randomly from the shipment. We have to find the probability that at most 1 lightbulb in a package of 10 lightbulbs is defective.The probability that a single light bulb in the package is defective is 0.01. The probability that in a package of 10 lightbulbs, at most 1 light bulb is defective is 0.9043.

So, the probability that a single light bulb in the package is not defective is (1-0.01) = 0.99.

Probability of at most one defective light bulb in a package of 10 lightbulbs:

P(X ≤ 1) = P(X = 0) + P(X = 1)

= (10C0 × 0.01⁰ × 0.99¹⁰) + (10C1 × 0.01¹ × 0.99⁹)

= (1 × 1 × 0.99¹⁰) + (10 × 0.01 × 0.99⁹)

= 0.9043 (approx.)

The probability that in a package of 10 lightbulbs, at most 1 light bulb is defective is 0.9043 (approx.).

Thus, the probability that in a package of 10 lightbulbs, at most 1 light bulb is defective is 0.9043.

This has been calculated using the binomial probability distribution formula.

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The account balance after 9 years is $528.28. The result is obtained by adding the interest to the initial deposit.

The simple interest of an amount of money can be counted by the following formula.

I = P₁ - P

I = P × r × t

Where

We have

Find the final account balance!

After 9 years, the simple interest of the savings is

I = P × r × t

I = $425.00 × 2.7% × 9 years

I = $3,825.00 × 0.027

I = $103.28

The final account balance would be

I = P₁ - P

$103.28 = P₁ - $425.00

P₁ = $425.00 + $103.28

P₁ = $528.28

Hence, after 9 years, the account balance would be $528.28.

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The student needs to score 61 marks on Paper 3 to achieve 64% of the total marks.

Calculate the total marks for Paper 1 and Paper 2 using the given percentages:

Paper 1: 65% of 60 marks

= 0.65 x 60

= 39 marks

Paper 2: 70% of 40 marks

= 0.7 x 40

= 28 marks

Determine the target total marks based on 64% of the total:

Target total marks

= 0.64 x 200

= 128 marks

So, Required marks on Paper 3

= Target total marks - (Marks from Paper 1 + Marks from Paper 2)

= 128 - (39 + 28)

= 128 - 67

= 61

Therefore, the student needs to score 61 marks on Paper 3 to achieve 64% of the total marks.

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a formula an for the -n- th term of the following sequence. assume the series begins can be represented by the formula an = (-1)^(n+1)(8 + 3n).



To find the formula for the -n- th term of the sequence, we need to observe the pattern in the given sequence. We can see that the sequence is alternating between positive and negative numbers, and the difference between the consecutive terms is increasing by 5.

Starting from the first term, 11, we can write the sequence as:

11 - 14 + 19 - 24 + ...

To find the pattern, we can write the terms in terms of their positions:

a1 = 11
a2 = -14
a3 = 19
a4 = -24

We can see that the sign of each term is alternating. To represent this in the formula, we can use (-1)^(n+1), which will give -1 for odd values of n and 1 for even values of n.

The other part of the formula should represent the increasing difference between the consecutive terms. We can see that the difference between the first two terms is 25, between the second and third terms is 33, and between the third and fourth terms is 43. We can observe that the difference between the consecutive terms is increasing by 8, which is 5 times the position of the term.

Therefore, the formula for the -n- th term of the sequence is:

an = (-1)^(n+1)(8 + 3n)


The formula for the -n- th term of the given sequence is an = (-1)^(n+1)(8 + 3n).

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Answer:

15 nickels and 11 quarters

The statement by Allison that size of the sample space of this compound event is 9 is incorrect because the size of sample space is 18.

The size of sample space for compound event of drawing one marble from bag and rolling number cube is actually 18, not 9.

There are 3 possible outcomes for drawing a marble = (red, blue, or green) and 6 possible outcomes for rolling number cube = (1, 2, 3, 4, 5, or 6),

So, the total number of possible outcomes for compound event is product of number of outcomes for each individual event = (3 × 6 = 18).

The sample space for compound event can be represented as an organized list, with each outcome listed as an ordered pair of form :

{(red, 1), (red, 2), (red, 3), (red, 4), (red, 5), (red, 6), (blue, 1), (blue, 2), (blue, 3), (blue, 4), (blue, 5), (blue, 6), (green, 1), (green, 2), (green, 3), (green, 4), (green, 5), (green, 6)}.

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The answer of the given question based on the Equation is given the solution to the given equation is n = 21/4.

A quadratic equation is type of equation in an algebra that involves variable (usually represented by x) that  raised to the second power (i.e., squared). The general form of the quadratic equation are given,

\(ax^2+bx+c = 0\)

The highest power of  variable is 2, hence , name "quadratic".

To solve this equation, we can start by simplifying each of the terms on both sides of the equation:

3n + √(n² + 8) + 3√(n² + 8) - √(n² + 8) = 8

Combining like terms, we get:

3n + 3√(n² + 8) = 8

Subtracting 3√(n² + 8) from both sides, we get:

3n = 8 - 3√(n² + 8)

Dividing both sides by 3, we get:

n = (8/3) - (√(n² + 8)/3)

Now, we can rearrange this equation to isolate the radical term on one side of the equation:

√(n² + 8)/3 = (8/3) - n

by Squaring both the sides of equation, we get:

n² + 8 = 64/9 - (16n/3) + n²

Simplifying this equation, we get:

16n/3 = 56/9

Dividing both sides by 16/3, we get:

n = 21/4

Therefore, the solution to the given equation is n = 21/4.

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Answer:

Step-by-step explanation:

Challenge # 1

Line has a negative slope with positive slope.

Therefore, equation will be,

y = 1.5x - 6

Parallel line to the given line will have same slope = 1.5 but with different y-intercept.

Equation of the parallel line → y = 1.5x + 6

Challenge # 2

Line has a negative y-intercept = -1 (Approx.)

Slope of the line = negative

Therefore, equation of the line will be,

y = -3.7x -1

Line parallel to the given line will have same slope but different y-intercept.

Equation of the parallel line → y = -3.7x + 1

Challenge # 3

Line with negative slope and no y-intercept.

y = -0.8x

Parallel line to the given line will have same slope and different y-intercept.

Equation of the parallel line → y = -0.8x + 1

Challenge # 4

Line in the graph has positive slope and negative y-intercept.

y = -5 + 4.2x

Line parallel to the given line will have same slope but different y-intercept.

Equation of the parallel line → y = - 7 + 4.2x

The average speed required to make the flight is about 47.62 miles per hour.

You're able to travel 20 miles/hour for 15 minutes, which means you cover 5 miles in 15 minutes. Therefore, the remaining 20 miles must be covered in 25 minutes.In this case, you can use the formula:
distance = speed x time = 20 miles/hour
t = 15 minutes (or 0.25 hours)
distance = 5 miles
You can use the formula to calculate the remaining distance:
d = s x t
s = d/t
Therefore, s = d/t
Therefore, the speed required for the remaining distance can be calculated as:
s = d/ts = 20 miles/hour
d = 20 miles (remaining distance)
t = 25 minutes (or 0.42 hours)
Substituting these values into the formula:s = 20 miles/0.42 hourss ≈ 47.62 miles/hour

The average speed required to make the flight is about 47.62 miles per hour.

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Answer:

4(b * x)

Step-by-step explanation:

The height of the tree and the building are 7.6 m and 28.6 m respectively.

An equation is an expression that shows the relationship between two or more variables and numbers.

Two triangles are similar if they have the same shape and the ratio of their corresponding sides are in the same proportion.

Triangle BGD, CHD and AFD are similar triangles.

CH = 1.6, DH = 8, GH = 30,  GF = 105

FH = GF + GH = 105 + 30 = 135

FD = FH + DH = 135 + 8 = 143; GD = 30 + 8 = 38

Hence, using similar triangles:

BG/CH = GD / DH

BG / 1.6 = 38/8

BG = 7.6 m

Also:

building/CH = DF / DH

building / 1.6 = 143/8

building = 28.6 m

The height of the tree and the building are 7.6 m and 28.6 m respectively.

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