A 40 cm spring will stretch one-sixth of the weight (in pounds) attached to it. Write a function to represent the situation.

Answer:

0.1 > 10^-2

(I'm pretty sure I'm right. sorry if im wrong :(

Answer:

2    4     6      8       10

1     2    3      4       5

Step-by-step explanation:So if it's filling up 2 gallons per minute then you would multiply  2x2=4 3x2=6 4x2=8 and 5x2=10. So you would multiply every minute by 2.

Answer:

Clockwise : going the way the clock hand goes (going right)

Counterclockwise : opposite of clock hand (going left)

Two questions about systems aaa and bbb, the given system is:

System aaa: x = -1/3 and y = -7/3
System bbb: x = -1/3 and y = -7/3

To answer two questions about systems aaa and bbb, let's first clarify the given system:

System aaa:
x - 4y = 9

System bbb:
2x + y = -3

Question 1: Solve system aaa.
To solve system aaa, we'll use the method of substitution:

Step 1: Solve one equation for one variable.
From the first equation in system aaa, we can isolate x:
x = 4y + 9

Step 2: Substitute the expression from Step 1 into the other equation.
Substitute the expression for x in the second equation of system aaa:
2(4y + 9) + y = -3

Step 3: Simplify and solve for y.
8y + 18 + y = -3
9y + 18 = -3
9y = -3 - 18
9y = -21
y = -21/9
y = -7/3

Step 4: Substitute the value of y into the expression for x.
Using the first equation in system aaa:
x - 4(-7/3) = 9
x + 28/3 = 9
x = 9 - 28/3
x = (27 - 28)/3
x = -1/3

Therefore, the solution to system aaa is x = -1/3 and y = -7/3.

Question 2: Solve system bbb.
To solve system bbb, we'll use the method of substitution:

Step 1: Solve one equation for one variable.
From the second equation in system bbb, we can isolate y:
y = -2x - 3

Step 2: Substitute the expression from Step 1 into the other equation.
Substitute the expression for y in the first equation of system bbb:
x - 4(-2x - 3) = 9

Step 3: Simplify and solve for x.
x + 8x + 12 = 9
9x + 12 = 9
9x = 9 - 12
9x = -3
x = -3/9
x = -1/3

Step 4: Substitute the value of x into the expression for y.
Using the second equation in system bbb:
y = -2(-1/3) - 3
y = 2/3 - 3
y = 2/3 - 9/3
y = -7/3

Therefore, the solution to system bbb is x = -1/3 and y = -7/3.

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To find the length of the diagonal fence that stretches from one corner to the opposite corner of a rectangle, we can use the Pythagorean theorem, which states that the square of the length of the diagonal (hypotenuse) is equal to the sum of the squares of the lengths of the two other sides (legs) of the rectangle.

In this case, the rectangle has dimensions 24 meters by 45 meters. Therefore, the length of the diagonal fence is:

Diagonal fence = √(24^2 + 45^2) meters

Simplifying the equation, we get:

Diagonal fence = √(576 + 2025) meters

Diagonal fence = √2601 meters

Diagonal fence = 51 meters

So Steve will need 51 meters of fencing to stretch diagonally from one corner to the opposite corner of his backyard.

Answer:

C.

Step-by-step explanation:

To calculate the value of X that Ellen should deposit in the bank, we need to determine the present value of the future payments that will accumulate to $50,000 in six years.

Using the formula for compound interest, the present value can be calculated as follows:

PV = X/(1 + r)^1 + X/(1 + r)^2 + X/(1 + r)^3,

where r is the annual interest rate (5%) expressed as a decimal.

To find the value of X, we set the present value equal to $50,000 and solve for X:

50,000 = X/(1 + 0.05)^1 + X/(1 + 0.05)^2 + X/(1 + 0.05)^3.

Once we determine the value of X, we can proceed to the next step.

For the second part of the question, after four years, the bank raises the interest rate to 6%.

From year four to year six, Ellen's money will continue to accumulate interest.

To find the amount donated, we calculate the future value of the remaining amount after deducting the down payment of $50,000:

Remaining amount = X/(1 + 0.06)^2 + X/(1 + 0.06)^3 + X/(1 + 0.06)^4.

The donated amount is then the difference between the remaining amount and the total accumulated after six years.

By evaluating these expressions, we can determine the value of X and the amount donated by Ellen.

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Answer:

I think the answer is B. I hoped I helped a little

Answer:

u=27 v=9.5 w=28.5

Step-by-step explanation:

The theorem states that if T is a translation along a line l, then T is also a translation along any line l' that is parallel to l.

To prove the theorem, let's consider a translation T along a line l. By definition, a translation preserves distances and directions. Now, let's consider a line l' that is parallel to l.

Since l' is parallel to l, any point on l' will have the same distance and direction from the corresponding point on l. In other words, for any point P on l', there exists a corresponding point Q on l such that the distance and direction between P and Q are the same.

Now, when we apply the translation T along l, it will move every point on l by the same distance and in the same direction. Since l' is parallel to l, the corresponding points on l' will also be moved by the same distance and in the same direction. Therefore, T is also a translation along l'.

Hence, we have proved that if T is a translation along a line l, then T is also a translation along any line l' that is parallel to l.

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Answer:

C or number 3

Step-by-step explanation:

The statement that "0.2 < 0.8 < 0.801 < 0.9" is true. The correct answer is option C.

To determine which statement is true, let's compare the given numbers:

0.8, 0.2, 0.9, 0.801

A. 0.8 < 0.2: False (0.8 is not less than 0.2)

0.9 < 0.801: False (0.9 is not less than 0.801)

Therefore, statement A is false.

B. 2 < 0.8: False (2 is not less than 0.8)

0.9 < 0.801: False (0.9 is not less than 0.801)

Therefore, statement B is false.

C. 0.2 < 0.8: True (0.2 is less than 0.8)

0.8 < 0.801: True (0.8 is less than 0.801)

0.801 < 0.9: True (0.801 is less than 0.9)

Therefore, statement C is true.

D. 0.2 < 0.9: True (0.2 is less than 0.9)

0.9 < 0.8: False (0.9 is not less than 0.8)

Therefore, statement D is false.

Based on the comparisons, the statement that is true is:

C. 0.2 < 0.8 < 0.801 < 0.9

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The correct question is as follows:

Which of the following statements is true?

A. 0.8 0.2 < 0.9 <0.801

B. 2 <0.8 < 0.9 <0.801

C. 0.2 <0.8 <0.801 <0.9

D. 0.2 < 0.9 <0.8 <0.801.

Answer: 13/25

Step-by-step explanation: it is equal to 52% which is greater than 50%

50% is greater than 13/25. To compare these two values, you can convert both of them to a common denominator, such as 50%. 50% is equal to 1/2, so 13/25 is equal to 52/50, which is less than 1/2 or 50%. Alternatively, you can also express both fractions as decimals and compare the two values that way. 50% is equal to 0.5, and 13/25 is equal to 0.52, so 50% is still greater than 13/25.

Answer:

16.1 ft of rope

Step-by-step explanation:

2.3 x 7=16.1

Answer:

16.1 feet per minute

Step-by-step explanation:

7×2=14

7×.3=2.1

2.1+14=16.1

Answer:

The difference between the two throws is 6/7 yards

Step-by-step explanation:

Beatrice throw=1 7/14 yards

Tilly throw=9/14 yards

Difference between the two throws=Beatrice throw - Tilly throw

=1 7/14 - 9/14

=21/14 - 9/14

= 21-9/14

=12/14

=6/7 yards

The difference between the two throws is 6/7 yards

A graph that correctly displays the data include the following: C. a histogram titled favorite topping with the x axis labeled topping and the y axis labeled number of customers, with the first bar labeled sprinkles going to a value of 17, the second bar labeled nuts going to a value of 12, the third bar labeled hot fudge going to a value of 27 ,and the fourth bar labeled chocolate chips going to a value of 44.

In Mathematics and Geometry, a histogram can be defined as a type of chart that is used to graphically represent a group of data points (statistical information) into user-specified ranges through the use of rectangles or rectangular bars.

Based on the information provided about the random sample of 100 customers at a local ice cream shop that were asked what their favorite topping, we can reasonably infer and logically deduce that a graph that correctly displays the data is a histogram.

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could be 17. not sure i´d wait for someone smarter than me to answer.

The vectors u and v are orthogonal when k equals 5 or -2.

Two vectors u and v are orthogonal if their dot product is equal to zero. The dot product of two vectors u and v is given by the formula:

u · v = u₁ × v₁ + u₂ × v₂ + u₃ × v₃

where u₁, u₂, u₃ are the components of vector u, and v₁, v₂, v₃ are the components of vector v.

Let's calculate the dot product of u and v:

u · v = (k × -5) + (k × (k + 2)) + (-2 × 5)

= -5k + k² + 2k - 10

= k² - 3k - 10

For the vectors to be orthogonal, the dot product must be zero:

k² - 3k - 10 = 0

To solve this quadratic equation, we can factor it or use the quadratic formula:

(k - 5)(k + 2) = 0

From this equation, we can see that the values of k that satisfy the equation are:

k = 5 or k = -2

Therefore, the vectors u and v are orthogonal when k equals 5 or -2.

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Answer:

Step-by-step explanation:

-4 is really  -1 * 4

-4² = -1 * 4²

-4² = -1 * 16

-4² = -16

Use parenthesis  to square

(-1 * 4)² = (-4)²

(-4)² = 16

Answer:

Al evento entraron 82 adultos y 18 menores de edad.

Step-by-step explanation:

De acuerdo a la información proporcionada, puedes plantear las siguientes ecuaciones:

x+y=100 (1)

90x+45y=8190 (2), donde:

x es el número de adultos

y es el número de menores de edad

Puedes despejar x en (1):

x=100-y (3)

Después, puedes reemplazar (3) en (2):

90(100-y)+45y=8190

9000-90y+45y=8190

9000-8190=90y-45y

810=45y

y=810/45

y=18

Ahora, puedes reemplazar el valor de y en (3) para encontrar x:

x=100-y

x=100-18

x=82

De acuerdo a esto, la respuesta es que al evento entraron 82 adultos y 18 menores de edad.

Step-by-step explanation:

What is the equivalent improper fraction of the multiplicand in the given 7 1/7 x 4 1/5?

this answer is 7 1/7 x 4 1/5=30

Answer:

y=3/2x-4

Step-by-step explanation:

3x-2y=8

-2y=-3x+8

y=3/2x-4

y=3/2x-4

3x-2y=8

-2y=3x+8

y=3/2x-4

Answer:

4:7, 16:28, 32:56, 64:112

Step-by-step explanation:

You can go down 1, and you can also keep doubling. I hope this helped, I hope you get it right! Have a Good Day!

The probability that it is in a winning position will be 0.8036.

Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.

Then the probability is given as,

P = (Favorable event) / (Total event)

A coin that is 2 cm in diameter is tossed onto a grid of squares each having a side length of 4 cm. A coin is in a winning position if no part of it touches or crosses a grid line, otherwise it is in a losing position.

Then the probability of winning is calculated as,

P = [a² - πd² / 4] / (a²)

P = [4² - 3.14 x 2² / 4] / (4²)

P = (16 - 3.14) / 16

P = 0.8036

The probability that it is in a winning position will be 0.8036.

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Answer:

2x-6=0

2x=6

x=6/2

x=3

..

The equation of the line are :

(a) y = x + 1, (b) 4y = 3x - 1, (c) y = -x + 1, (d)  y = -2x + 1 and (e) y = 2x.

Slope intercept form of the line is y = mx + c, where m is the gradient and c is the y intercept.

Point slope of the line is (y - y') = m (x - x'), where m is the gradient and (x', y') is a point.

(a) Equation of the line through (2, 3) and gradient 1.

Substituting in point slope form,

y - 3 = 1 (x - 2)

y - 3 = x - 2

y = x + 1

(b) Equation of the line through (-1, -1) and gradient 3/4.

y - -1 = 3/4 (x - -1)

y + 1 = 3/4 x + 3/4

y = 3/4 x - 1/4

4y = 3x - 1

(c) Equation of the line through (1, 0) and (-2, 3).

Slope, m = (3 - 0) / (-2 - 1) = -1

y intercept = 1

y = -x + 1

(d) Equation of the line through (0, 1) and (-1, 3).

Slope, m = (3 - 1) / (-1 - 0) = -2

y - 1 = -2 (x - 0)

y = -2x + 1

(e) Equation of the line through (1, 2) and parallel to the line with gradient 2.

Two parallel lines have the same slope.

y - 2 = 2 (x - 1)

y = 2x

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Answer:

The required equation is:

Step-by-step explanation:

We know that

distance = rate × t

Given that a car moving at a constant speed passed a timing device at t=0.

In other words, at t = 0 second, d = 0 ft.

After 7 ​seconds, the car has traveled 567 ft.

In other words, at t = 7 seconds, d = 567 ft

Thus, there are two points

(0, 0)

(7, 567)

Finding the slope between (0, 0) and (7, 567)

Using the formula

Slope = Rate of change = [y₂-y₁] / [x₂-x₁]

                                        = [567 - 0] / [7-0]

                                        = 567 / 7

                                        = 81 ft/second

Given that the car is moving at constant speed. So, we dont't have any other factor or term to consider

Thus, the required equation is:

distance = rate × t

d = 81 × t

d = 81t

or

f(t) = 81t

VERIFICATION

Given the equation

d = 81 × t

Put t = 0 to find the disatance in 1 sec

d = 81 × (0) = 0 ft

Put t = 7 to find the distance in 7 seconds

d = 81 × (7) = 567 ft

Answer:

24, 897.12178 mi

Step-by-step explanation:

diameter is 7,925 mi

circumference = diameter *pi = 7,925*3.14= 24, 897.12178 mi

Answer:

d=7925mi

circumference of circle=πd

=3.14×7925

=24884.5 mi