Bert wears a pedometer that tracks the number of steps he takes. Before mowing the lawn this morning, he predicted he'd take 1,800 steps while doing the job. His prediction was 4% lower than the actual number of steps he took. How many steps did Bert actually take while mowing the lawn? ​

Part A: The vertex, domain, and range of the function are respectively; (5, 0), ( - ∞ , ∞ ),  [0, ∞ ]\

Part B: The function f(x) = |x| is vertically shifted by 3 units to get the function h(x) = |x| + 3. The y-coordinate of the vertex is shifted by 3 units.

Part A: The given function is g(x) = | x - 5 |.

The x-coordinate of the vertex will be: x - 5 = 0

x = 5

Therefore, the y-coordinate of the vertex will be:

y = g(x) = |x - 5|

y = g(5) = |5 - 5|

y = 0

So, the absolute value vertex is (5, 0).

Now, all real numbers fall under the expression's domain, with the exception of cases where it is undefined. In this instance, the phrase is defined even if there is no real number. Thus;

Interval Notation: ( - ∞ , ∞ )

Set builder Notation: { x | x ∈ R }

The set of all legitimate y values is the range.

Interval Notation: [0, ∞ ]

Set builder Notation: { y | y ≥ 0}

Part B: h(x) = |x| + 3 is the transformed version of the parent function f(x) = |x|.

For the parent function f(x) = |x|, the vertex is ( 0, 0).

The range of an absolute function in the form c( | ax + b | ) + k is f(x) ≥ k.

Therefore, the range of the function f(x) = |x| is f(x) ≥ 0 and in interval notation is [ 0, ∞ ).

For the transformed function h(x) = |x| + 3.

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

The range of function is h(x) ≥ 3 and in interval notation is [3, ∞ ).

Hence, the y coordinate of the vertex is transformed by 3.

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1) The investment's balance (future value) after 15 years, assuming no further deposits or withdrawals, for the first account modeled by the equationy=5000⋅1.05^x, is $10,395.

2) Assuming no other deposits or withdrawals occurred, the initial investment (present value) for the second account modeled by the equation 3257.79=p⋅1.05^10 is $2,000.

The future value is the present value or periodic investments compounded at an interest rate.

The future value can be computed using an online finance calculator or the FV factor.

The present value is the future value or periodic inflows discounted at an interest rate.

Similarly, the present value can be computed using an online finance calculator or the PV factor.

Equation 1: y=5000⋅1.05^x

Initial investment = $5,000

Annual interest rate = 5%

Investment period = 15 years

Future value factor for 15 years at 5% = 2.079

N (# of periods) = 15 years

I/Y (Interest per year) = 5%

PV (Present Value) = $5,000

PMT (Periodic Payment) = $0

Results:

FV = $10,395 ($5,000 x 2.079)

Total Interest = $5,395

Equation 2: 3257.79=p⋅1.05^10:

Future value = $3,257.79

Annual interest rate = 5%

Investment period = 10 years

Present value factor for 10 years at 5% = 0.641

N (# of periods) = 10 years

I/Y (Interest per year) = 5%

PMT (Periodic Payment) = $0

FV (Future Value) = $3,257.79

Results:

PV (Present Value) = $2,000 ($3,257.79 x 0.641)

Total Interest = $1,257.79

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7

it could be 7 because if you think about it, 4 can't go into 7 evenly.

so the proper way to solve this would be by finding how many times 4 can go into 7 evenly

4 can go into 7 once evenly

3 times 1 is 3

so you would have 4 left over

1 r4

The axis of symmetry of the function is x = 0

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

y = -x^2 - 0.1

Differentiate the function

So, we have the following representation

y' = -2x

Set the differentiated function to 0

This gives

-2x =0

Divide both sides by -2

x = 0

Hence, the axis of symmetry is x = 0

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The inequality that represents the graph will be y ≤ -(3/4)x + 2.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

The line is passing through points (0, 2) and (4, -1). Then the equation of the line is given as,

(y - 2) = [(- 1 - 2) / (4 - 0)](x - 0)

y - 2 = -(3/4)x

y = -(3/4)x + 2

The region below the line and points on the line is considered. Then the linear inequality is written as,

y ≤ -(3/4)x + 2

The inequality that represents the graph will be y ≤ -(3/4)x + 2.

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The summation notation for the series is given as follows:

C. [tex]\sum_{i = 1}^{8} \frac{(-1)^i}{2i}[/tex]

The summation series for this problem is defined as follows:

-1/2 + 1/4 - 1/6 + ... - 1/16.

For the numerator, which is the top term of the fractions, we have that:

The sign of each term is controlled by the numerator, which is defined as follow:

(-1)^i.

For the denominator, we have that it is multiplied by two for each new term, starting at two, hence the rule is given as follows:

2i.

This means that the summation notation for the series is given as follows:

[tex]\sum_{i = 1}^{8} \frac{(-1)^i}{2i}[/tex]

Meaning that the correct option is given by option C.

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In 8 1/2 hours, the candle would burn  6 3/8 inches.

A mixed number is a non-integer that is made up of a whole number and a proper fraction. An example of a mixed number is 8 1/4.

The first step is to determine how much of the candle burns in one hour.

Inches of candle that burns in 1 hour = 8 1/4 ÷ 11

33/4 x 1/11 = 3/4 inches

Now, multiply the inches of candle that burns in an hour by 8 1/2

Inches of candle that would burn in 8 1/2 hours = 3/4 x 8 1/2

3/4 x 17/2 = 51/8 = 6 3/8 inches

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The best price can be obtained by taking the ratio and it is given for the case of two weeks ago.

The ratio of two numbers a and b can be written as a : b = a/b.

The ratio of two quantities is the unit rate of one quantity with respect to the other.

The price of gas per gallon for both the cases are calculated as below,

Two weeks ago it is given as,

Total price ÷ Number of gallons

⇒ 31.14 ÷ 9 = $3.46

And, for last week it is given as,

Total price ÷ Number of gallons

⇒ 52.70 ÷ 15 = 3.51

Thus, the price per gallon is cheaper two weeks ago.

Hence, the best price of gas is obtained for the case of two weeks ago.

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The domain of the quadratic function is (-∞,∞). The range of the quadratic function is (-∞,3].

What is interval notation?

Interval Notation is a method of representing a subset of real numbers by the numbers that connect them.

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

The function extended downward direction in a vertical. The function extended on both sides of the x-axis horizontally.

The x-coordinate of the points on the quadratic function is the domain.

The y-coordinate of the points on the quadratic function is the range.

The x-coordinate of the points on the quadratic function is from -∞ to ∞.

The y-coordinate of the points on the quadratic function is from -∞ to 3.

The domain of the function is (-∞,∞).

The range of the function is  (-∞,3].

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Based on the information, it can be inferred that the order from lightest to heaviest lure would be: 0.25 (c), 0.372 (d), 0.5625 (b), and 0.625 (a).

To calculate the weights of the lures we must take into account that they are fractional, that is to say that to find an exact number of the weight of each one of the lures we can carry out the division of the fractional to have a decimal number that allows us to organize more easily the pesos.

According to the above information, the weights would be the following:

a. 5/8 = 0.625

b. 9/16 = 0.5625

c. 1/4 = 0.25

d, 3/8 = 0.372

Then, the weights organized from smallest to largest would look like this: 0.25 (c), 0.372 (d), 0.5625 (b), and 0.625 (a).

Note: This question is incomplete because there is some information missing. Here is the complete information:

Options:

a. 5/8OZ

b. 9/16 OZ

c. 1/4OZ

d. 3/8OZ

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The particle increases its velocity in the following three subintervals:

In this question we find the case of the position of a particle (x) in versus time (t), whose graph is shown below. The velocity associated to a given time t is represented by the slope of the line tangent to that point. The velocity of a particle increases when the signs of function position and function velocity are the same.

By secant line formula, velocity can be approximated by this formula:

v ≈ Δx / Δt

Since time is a non-negative real number, the sign of velocity is derived by the following rules:

Then, the velocity of the particle increases in the following two cases:

The velocity is increasing in the following subinterval 0 < t < 2, 4 < t < 7 and 9 < t < 10.

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The total area of the shape is 129 square feet.

A rectangle is a part of a quadrilateral, whose sides are parallel to each other and equal.

In the given diagram, there are two shapes,

One is rectangle whose sides are 16 feet and 5 feet.

And other is square whose side is 7 feet.

Since, the area of rectangle = length x width = 16 x 5 = 80 square feet.

And area of square = (side)² = (7)² = 49 square feet.

Total area of shape = area of rectangle + area of square

= 80 + 49

= 129 square feet.

The total area of the shape is 129 square feet.

Hence, the total area of the shape is 129 square feet.

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Step-by-step explanation:

plsssssssssssssssssssssssssssssssssssssssssssssssssssssssdssssssssssssssssssssssssssssssssssssssssss do it don't be lazy.

The coordinates of the equation are (-2, -7), (-1, -5), (0, -3), (1, -1) and (2, 1)

The value of x and y in the given equation or in the graph is together represented by (x, y) and called coordinates.

Given is an equation, y = 2x-3

And we have x values = -2, -1, 0, 1 and 2, To find the corresponding value of y, we will use one by one the values of x in the equations,

When, x = -2,

y = -2(2) - 3

y = -7

(-2, -7)

When x = -1

y = 2(-1) - 3

y = -5

(-1, -5)

When x = 0

y = 2(0) - 3

y = -3

(0, -3)

When x = 1

y = 2(1)-3

y = -1

(1, -1)

When x = 2

y = 2(2) - 3

y = 1

(2, 1)

Hence, the value of y are -7, -5, -3, -1 and 1

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The value of p + q is 17.

The probability that one of the three risk factors will be present in exactly the right amount for a randomly chosen individual can be calculated using the inclusion-exclusion principle. The probabilities that a man has risk factors A (but not B or C), B (but not A or C), and C (but not A or B) are, accordingly, denoted by the letters P(A), P(B), and P(C). Next, we have:

P(A or B or C) = P(A) + P(B) + P(C) - P(A and B) - P(A and C) - P(B and C) + P(A and B and C)

P(A) = P(B) = P(C) = 0.1 and P(A and B) = P(A and C) = P(B and C) = 0.14 are both supplied to us.

 Additionally, it is stated that if a guy possesses both A and B, there is a 1/3 chance that he possesses all three risk factors. Using this knowledge, we can calculate P. (A and B and C).

P(A, B, and C) = P(A, B | C) * P(C) = (1/3) * 0.1 = 1/30 is what we got.

These values are then reinserted into the equation above to produce the following result: P(A or B or C) = 0.1 + 0.1 + 0.1 - 0.14 - 0.14 - 0.14 + 1/30 = 0.44/30 = 11/75

None of the three risk factors are present in a guy in a likelihood of 1 - P(A or B or C) = 1 - 11/75 = 64/75. As a result of the reduction of the proportion 64/75 to 8/9, p = 8 and q = 9, and p + q = 8 + 9 = 17.

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Answer: C’(3,-4)

Step-by-step explanation: All you have to do is count how many blocks away is the point from the x axis and then count down the x axis where you stop counting and that is how you get your point.

The coordinates of the focus of the parabola is calculated as; (0, 2).

We are told that the shape of a satellite dish can be described as parabolic. This is due to the fact that radio waves are reflected from the surface of the dish and received into the focus.

The path of the object shown in a plane curve generated by a moving point is called a parabola.

The general equation of a parabola is;

x² = 4ay

Where a is the focus of the parabola.

The given equation of the parabola is;

x² = 8y

The coordinate of the focus of the parabola is of the form; (0, a).

Comparing both equations, we have that the focus of the parabola is;

4a = 8

a = 8/4

a = 2

Hence, we conclude that the coordinate of the focus of the parabola is (0, 2).

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Answer:

The answer is 1.25.

Step-by-step explanation:

You can see what sides match up, and then you divide to find the scale factor.

17.5/14 = 1.25

20/16 = 1.25

The opposite of the number 19(4/3) is

Additive inverse is the opposite of a number in terms of addition, this is the number that gives zero when added to the original number.

To get a result equal to 0, add the original number and the additive inverse or by simply changing the sign of the integer. On the basis of negation of the original number.

In the problem, the opposite of 19(4/3) is solved as follows

let x be the opposite

19(4/3) + x = 0

x = -19(4/3)

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Liters of fuel in 1 hr is S/E and Liters of fuel in 60 km is 60/E

Liters of fuel in 1 hr: The Quasi JX travels E kilometers per liter of fuel (EkmL)(EkmL) at S kilometers per hour (Skmhr)(Skmhr). Therefore the Quasi JX requires 1E1E liters of fuel to travel 1 km. Since the Quasi JX travels S kilometers per hour, it requires 1E1E LkmLkm × S km/hr, or SELhrSELhr

Thus, Liters of fuel in 1 hr is S/E.

Liters of fuel in 60 km: The Quasi JX travels E kilometers per liter of fuel (EkmL). Therefore the Quasi JX requires 1E1E liters of fuel to travel 1 km. Given this, the Quasi JX uses 1/E L/km × 60 km, or 60/E L of fuel to travel 60 km.

Thus, Liters of fuel in 60 km is 60/E.

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The expression that represents the number of liters of fuel used in a 60 km drive under ideal driving conditions at a constant speed S is written as 60/E

Here we have given that RO1, Liters of fuel in 1 hour

Here we also know that the Quasi JX travels E kilometers per liter of fuel (E km/L) at S kilometers per hour (S km/hr)

Now, we have to know that the Quasi JX requires 1/E liters of fuel to travel 1 km.

Here the JX travels S kilometers per hour, and here it requires

=> (1/E x L/km) × (S km/hr)

Then it can be written as when we apply the value of Ro1 is 60, then we get

=> 60/E

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Answer:

To reflect, place points at

5, -2

2, -2

2, -5

5, -5

Step-by-step explanation:

Answer:

Step-by-step explanation:

graphs above x-axis are positive and below are negative.

(b). A(+), B(+), C(-),D (-)

A=(3-0)/(1-0)=3

B=(1-0)/(2-0)=1/2

C=(-6-0)/(1-0)=-6

D=(-1-0)/(4-0)=-1/4

(c). 3>1/2>-1/4>-1/6

so 3 is greatest value.

Answer:

Step-by-step explanation:

25% = 25/100 = 0.25

Then:

Bounce 1:

160 - (160*0.25) = 160 - 40 = 120

Bounce 2:

120 - (120*0.25) = 120 - 30 = 90

Bounce 3:

90 - (90*0.25) = 90 - 22.5 = 67.5

Bounce 4:

67.5 - (67.5*0.25) = 67.5 - 16.875 = 50.625

Answer:

a) y = 2,035(1.03)^t

b) 2,359

Step-by-step explanation:

a)

Exponential growth:

y = a(1 + r)^t

where

y = future vale

a = initial value

r = periodic rate of growth

t = number of periods

y = 2,035(1 + 0.03)^t

y = 2,035(1.03)^t

b)

Here we have a = 2,035; r = 3% = 0.03; t = 5

y = 2,035(1 + 0.03)^5

y = 2,359

2,359

The total number of ways in which the selection can be done are 3.

Given is to take out 2 objects without replacement from 3 objects, pencil, eraser, and desk.

The total number of ways in which the selection can be done is -

C(3, 2) = (3!)/(2!)(1!) = 3

C(3, 2) = 3

Therefore, the total number of ways in which the selection can be done are 3.

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For any real number c, it is calculated that √(c²) is; Option D: c

The set of real numbers is defined as the union of the set of Irrational numbers and the set of rational numbers.

Now, we are given the equation as;

√(c²)

Now, from definition of real numbers, it means that they are not imaginary and as such any value of c remains the same. Thus, we have;

√(c²) = c

Now, because c is not classified as an absolute value, and even if since it is square, will be surely positive and as such the final answer for every real number c in the square root will be c.

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Answer:12

Step-by-step explanation:4/3x-2/3x=2/3x

6+2=8

2/3x=8

x=12

Answer:

X = 12

Step-by-step explanation:

2​x+2=34​x−6

Multiply both sides of the equation by LCM

(32​x+2)×3=(34​x−6)×3

CalculateMore Steps

 2x+6=(34​x−6)×3

CalculateMore Steps

 2x+6=4x−18

Move the variable to the left side

2x+6−4x=−18

Subtract the termsMore Steps 

−2x+6=−18

Move the constant to the right side

−2x=−18−6

Subtract the terms

−2x=−24

Multiply both sides

−2x(−21​)=−24×(−21​)

SimplifyMore Steps

 −2x(−21​)=12

Solution

x=12

The terms of the expression are 4, 2(5) and -3 and the value of the expression is 11

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

4 + 2(5 + (-3)

Rewrite properly

So, we have

4 + 2(5) + (-3)

For an expression ax + by

The terms are ax and by

This means that the terms of 4 + 2(5) + (-3) are 4, 2(5) and -3

Here, we have

4 + 2(5) + (-3)

Remove the brackets

4 + 2(5) + (-3) = 4 + 10 - 3

Evaluate the like terms

4 + 2(5) + (-3) = 11

Hence, the value is 11

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The values of l and h, along with w for the rectangular pyramid, that will produce identical volumes, are given by the following relation:

w = 4l.

(the value of the height is free).

The volume of a pyramid is calculated as the multiplication of the base area by the height, which is then divided by three.

Hence, the formula is given as follows:

V = Ab x h/3.

In which:

The base areas are calculated as follows:

Four congruent square pyramids whose combined volume is the same as the volume of a single rectangular pyramid, hence the relation is given as follows:

4l²h/3 = lwh/3.

w = 4l.

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The expression which shows how much additional money generated at an interest rate of 5% than at an interest rate of 3% is: (1,000 (1 + 5 / 1,200) ^12) – (1,000 (1 + 3 / 1,200) ^12). The correct answer is option D.

The amount of money generated at the interest rate of 5% is shown by A₅ :

1,000 (1 + 5 / 1,200) ^12

And similarly, the amount of money generated at the interest rate of 3% is shown by A₃ :

1,000 (1 + 3 / 1,200) ^12

Hence, the additional amount of money will be shown by A₅ – A₃  :

(1,000 (1 + 5 / 1,200) ^12) – (1,000 (1 + 3 / 1,200) ^12)

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Although part of your question is missing, you might be referring to this full question: 1,000 (1 + r/1,200) ^12. The expression above gives the amount of money, in dollars, generated in a year by a $1,000 deposit in a bank account that pays an annual interest rate of r%, compounded monthly. Which of the following expressions shows how much additional money is generated at an interest rate of 5% than at an interest rate of 3%?

A. 1,000 (1 + (5 – 3) / 1,200) ^12

B. 1,000 (1 + (5 / 3) / 1,200) ^12

C. (1,000 (1 + 5 / 1,200) ^12) / (1,000 (1 + 3 / 1,200) ^12)

D. (1,000 (1 + 5 / 1,200) ^12) – (1,000 (1 + 3 / 1,200) ^12)

The pounds of expensive jelly beans that Mike should use, given the amount he wants to sell the mixture, is 30 pounds.

The total weight of the mixture is x + 10 pounds because Mike adding 10 pounds of the cheaper jelly beans while the cost of the expensive jelly beans would be:

= 5 x number of pounds

= 5x

The total cost of the cheaper jelly beans is :

= 10 pounds x 2

= $ 20

The total revenue from the mixture is therefore:

= 4.25x + 42.5

The total cost is :

= 5x + 20

Equating these would find the pounds of expensive jelly beans needed :

5x + 20 = 4.25x + 42.5

0.75x = 22.5

x = 30

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