A commuter train travels 50 kilometers in 43 minutesWhat is speed in kilometers per hour?

The amount that she make in a workweek if she sold $4,800 worth of merchandise will be $605.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

Here, Mae Ling earns a weekly salary of $365 plus a 5.0% commission on sales at a gift shop.

The amount that she make in a workweek if she sold $4,800 worth of merchandise will be:

= $365 + (5% × $4800)

= $605

The amount is $605.

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The roots of the equation are 9 + 3i and 9 - 3i in simplest a + bi form.

What is meant by roots?

A root is a value that satisfies an equation, for example, the solution of an equation when set equal to zero. The roots of an equation are often called solutions or zeros of the equation.

What is a equation?

An equation is a mathematical statement that shows that two expressions are equal. It usually consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division.

According to the given information

To find the roots of the equation x² - 18x + 90 = 0 in simplest a + bi form, we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

where a = 1, b = -18, and c = 90.Plugging in these values, we get:

x = (18 ± √((-18)² - 4(1)(90))) / 2(1)

x = (18 ± √(324 - 360)) / 2

x = (18 ± √(-36)) / 2

The discriminant (-36) is negative, which means that the roots are complex conjugates. Therefore, we can simplify the expression as follows:

x = (18 ± 6i) / 2

x = 9 ± 3i

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Answer:

11/15

Step-by-step explanation:

P('Y' or 'R') = 5/15 + 6/15 which is 11/15

Answer:

1.96

2.48

3.96

4.15

5.7.5

6. 15

Step-by-step explanation:

1. Line segment EQ bisects chord HI. This also means that it bisects Arc HI so that

Using that Arc HI= HQ times 2. HQ equal 48 so

\(48 \times 2 = 96\)

HI=96.

2. Since Arc HQ equal QI, QI measure is 48.

3. Since Both chrods are equidistant from the center of the circle, they are equal in length. Arc HI measures 96. Using the transitive property, Arc JK also measures 96.

JK=96

4. JR measures 7.5 so that means JK also measures 7.5. JK measure is 15. HI=JK so HI=15.

5.PI is half of HI so it measures 7.5

6. JK measures 15.

The maximum strut load is 70.87 kN. The maximum strut load can be calculated using the following equation: Maximum strut load = 2 * unit weight * gravity * depth * sin(friction angle) * cos(friction angle)

In this case, the unit weight is 20 kN/m3, the gravity is 9.81 m/s^2, the depth is 7.5 m, and the friction angle is 36°. Plugging these values into the equation, we get the following:

Maximum strut load = 2 * 20 * 9.81 * 7.5 * sin(36°) * cos(36°) = 70.87 kN

Therefore, the maximum strut load is 70.87 kN.

The maximum strut load occurs at the first row of struts, which is installed at a depth of 0.5 m below ground surface. The strut load decreases with depth, and the maximum strut load is reached at the first row of struts.

The strut load is caused by the weight of the soil above the struts. The soil above the struts exerts a lateral force, which is resisted by the struts. The maximum strut load occurs when the lateral force is at its maximum.

The maximum strut load is an important design consideration for braced cuts. The strut load must be able to be safely carried by the struts. If the strut load is too high, the struts may buckle or fail.

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Answer:

Exact Form:

32/5

Decimal Form:

6.4

Mixed Number Form:

6 2/5

Step-by-step explanation:

your gonna wanna if possible cancel the common factors.

A stochastic process X(t) is called a martingale if the expected value of X(t) given all information available up to and including time s is equal to the value of X(s).

Thus, to show that the process X(t):=e^(t/2)cos(W(t)), 0 ≤ t ≤ T is a martingale w.r.t. any filtration for Brownian motion, we need to prove that E(X(t)|F_s) = X(s), where F_s is the sigma-algebra of all events up to time s.

As X(t) is of the form e^(t/2)cos(W(t)), we can use Itô's lemma to obtain the differential form:dX = e^(t/2)cos(W(t))dW - 1/2 e^(t/2)sin(W(t))dt

Taking the expectation on both sides of this equation gives:E(dX) = E(e^(t/2)cos(W(t))dW) - 1/2 E(e^(t/2)sin(W(t))dt)Now, as E(dW) = 0 and E(dW^2) = dt, the first term of the right-hand side vanishes.

For the second term, we can use the fact that sin(W(t)) is independent of F_s and therefore can be taken outside the conditional expectation:

E(dX) = - 1/2 E(e^(t/2)sin(W(t)))dt = 0Since dX is zero-mean, it follows that X(t) is a martingale w.r.t. any filtration for Brownian motion.

Now, let's represent X(t) as an Itô process on the interval [0,T]. Applying Itô's lemma to X(t) gives:

dX = e^(t/2)cos(W(t))dW - 1/2 e^(t/2)sin(W(t))dt= dM + 1/2 e^(t/2)sin(W(t))dt

where M is a martingale with M(0) = 0.

Thus, X(t) can be represented as an Itô process on [0,T] of the form:

X(t) = M(t) + ∫₀ᵗ 1/2 e^(s/2)sin(W(s))ds

Hence, we have shown that X(t) is a martingale w.r.t. any filtration for Brownian motion and represented it as an Itô process on any time interval [0,T], T > 0.

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Answer:

THE CONSTANT OF VARIATION IS 1/2 or 0.5

Step-by-step explanation:

Here, we want to calculate the variation constant.

From the question, we are told that number of days varies directly as the number of chores

Mathematically, that would be;

y = kx

where k is the constant of proportionality

To get the value of k, we simply divide the value of y at a point by the value of x at that point

Mathematically;

1 = 2k

which is same as

5 = 10k

Thus, the value of k would be 5/10 = 1/2 or 0.5

Answer:

The answer is 1/2 so C

Step-by-step explanation:

Answer:

105?

Step-by-step explanation:

Answer:

43 just did it

Step-by-step explanation:

just did it

Answer: 28√5

Step-by-step explanation:

The endpoints of EF are E(-3 , 10) and F(5 , 6)

Let x1 = -3, y1 = 10, x2 = 5, y2 = 6

So, the length of EF is,

\(\begin{aligned}&\mathrm{EF}=\sqrt{\left(\mathrm{x}_{2}-\mathrm{x}_{1}\right)^{2}+\left(\mathrm{y}_{2}-\mathrm{y}_{1}\right)^{2}} \\&\mathrm{EF}=\sqrt{\left(5-(-3)^{2}+(6-10)^{2}\right.} \\&\mathrm{EF}=\sqrt{(5+3)^{2}+(-4)^{2}} \\&\mathrm{EF}=\sqrt{64+16} \\&\mathrm{EF}=\sqrt{80} \\&\mathrm{EF}=4 \sqrt{5}\end{aligned}\)

Scale factor = 7

Therefore,

\(\begin{aligned}&\mathrm{E}^{\prime} \mathrm{F}^{\prime}=7 \mathrm{EF} \\&\mathrm{E}^{\prime} \mathrm{F}^{\prime}=7 \cdot 4 \sqrt{5} \\&\mathrm{E}^{\prime} \mathrm{F}^{\prime}=28 \sqrt{5}\end{aligned}\)

Check the picture below.

notice, the function namely f(x) or "y", has a hole at (-3 , 2), that means that the values for the range are anything less than 2, but never 2, so 1.1 is ok, 1.99 is also good, 1.999999999999999 is also ok, but never 2, thus y < 2.

Let's also notice, the arrowhead means the graph keeps on going to the left as well as to the bottom.

The volume of the candle is approximately 94 cubic inches.

A circular cylinder is a three-dimensional solid object made up of two parallel and congruent circular bases and a curving surface connecting the bases.

The volume of a right circular cylinder is given by the formula:

V = πr²h

Where

Substituting the given values into the formula, we get:

V = 3.14 x 2² x 7.5

V = 3.14 x 4 x 7.5

V = 94.2

Rounding to the nearest cubic inch, we get:

V ≈ 94 cubic inches

Therefore, the volume of the candle is approximately 94 cubic inches.

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Given:

In 2001, the number of registrations = 56.1 thousand

In 2002, the number of registrations = 62.5 thousand

We will write the linear equation to represents the given situation

Let G the number of registrations

And t is the number of years where t = 0 is the year 2000

So, in year 2001, t = 1, G = 56.1

And in year 2002, t = 2, G = 62.5

The general form of the equation will be: G = m * t + b

Where: (m) is the slope

and (b) is the y-intercept which will be the number of registrations at t = 0

We will find the slope as follows:

Substitute with (m), so the equation will be:

Substitute with (t = 1, G = 56.1) to find (b)

So, the equation will be:

B) Graph the equation:

The graph of the equation will be as shown in the following picture:

C) we will find the number of registrations in 2017

so, t = 2017 - 2000 = 17

So, substitute with (t=17) into the equation to find G

so,

So, the number of golden retrievers = 158.5 thousand

Answer:

Under couch

Step-by-step explanation:

Answer:

d=6h

Step-by-step explanation:

Speed of the raft= 6 miles per hour

Total distance (d) of the raft= rate × number of hours

d=r*h

Independent variable is the number of hours(h)

Dependent variable is the distance (d)

Equation for the situation

d=r*h

d=distance

r=rate

h=number of hours

From the question,

r=6 miles per hour

Therefore,

The equation is

d=r*h

d=6*h

d=6h

The fence surrounds a square yard with an area of 64 square meters. We first have to find length of fence and then multiply it by itself.

Given that it took 48 square meters of lumber to build the fence, and the fence is 1.5 meters tall, we can calculate the area of the yard inside the fence. To do this, we need to determine the total length of the fence. If we assume that the fence is built around a square yard, then the length of each side of the yard will be equal to the total length of the fence divided by 4.

Let's call the length of each side of the yard x. Then, the area of the yard inside the fence is x * x, or x^2. The total length of the fence is 4 * x. Since the fence is 1.5 meters tall, the total area of the lumber used to build the fence is 4 * x * 1.5, or 6x. This is equal to 48 square meters, so we have the equation:

6x = 48.

Solving for x,

x = 8.

Therefore, each side of the yard is 8 meters long.

Area of the yard inside the fence = 8 * 8 = 64 square meters.

This means that the fence surrounds a square yard with an area of 64 square meters.

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Answer:

False

Step-by-step explanation:

15.026

1 = tens

5 = ones

0 = tenths

2 = hundredths

6 = thousandth

This number is read as fifteen and twenty-six thousandths.

So, the answer is False.

When swerving, there are a number of factors that come into play, including traction, lean, load triangle, and being upright. Swerving in a straight line can be relatively easy, as the rider only needs to make minor adjustments to maintain balance.

When comparing swerving in a straight line to swerving in a curve, the key differences involve traction and maintaining an appropriate lean angle.
Swerving in a curve requires more traction than swerving in a straight line. Traction is essential for maintaining control of your vehicle, especially when navigating curves. As you swerve in a curve, your tires need to have a good grip on the road surface to prevent skidding or losing control.
Additionally, managing lean angles is more critical when swerving in a curve. To maintain balance and control, you must avoid leaning too much, as it can cause the vehicle to tip over or slide out. In a curve, the lean angle needs to be adjusted appropriately to match the curve's radius, while also considering your speed and road conditions.
In summary, swerving in a curve requires more traction and careful management of lean angles compared to swerving in a straight line. The load triangle and keeping the vehicle upright are important, but they are not the primary factors that make swerving in a curve more challenging than swerving in a straight line.

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The price of a banana is 0.71 (after round off) USD per pound.

Here the price of a banana in Mexico was 34 pesos per kilogram.

price of a banana in Mexico = 34 pesos per kilogram

We are provided with the following information,

1 kg = 2.205 pounds,

and 1 Peso = 0.04574USD

We have to find the price in USD per pound,

So we have,

=(34 × 0.04574 )÷ 2.205

= 0.7105 USD per pound

= 0.71 USD per pound   (after round off)

Therefore the price of a banana in UDS per pound is 0.71 ( after round off) .

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Answer:

\(4.6\ \text{cm}\)

Step-by-step explanation:

Perimeter of the pentagon = 20.5 cm

Length of 4 sides = \(x\)

Length of the other side = 2.1 cm

Perimeter of the pentagon will be

\(x+x+x+x+2.1=20.5\\\Rightarrow 4x+2.1=20.5\\\Rightarrow 4x=20.5-2.1\\\Rightarrow 4x=18.4\\\Rightarrow x=\dfrac{18.4}{4}\\\Rightarrow x=4.6\ \text{cm}\)

The value of \(x\) is \(4.6\ \text{cm}\).

Using proportions, it is found that:

A. 0.5 pounds of butter.

B. 1.25 gallons of cream.

Item a:

The rule of three is:

0.5 gallon of cream - 1 pound of butter

0.25 gallons of cream - x pounds of butter

Applying cross multiplication:

\(0.5x = 0.25\)

\(x = \frac{0.25}{0.5}\)

\(x = 0.5\)

Thus, you could make 0.5 pounds of butter.

Item b:

0.5 gallon of cream - 1 pound of butter

x gallons of cream - 2.5 pounds of butter

\(x = 2.5(0.5) = 1.25\)

You would need 1.25 gallons of cream.

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Answer:

374mm squared

Step-by-step explanation:

Bottom rectangle can be cut off to equal 52mm, by multipling 4 by 13

the rest is 14*23, which equals 322mm

add those together to get 374mm squared

Answer:

374 square millimeters

Step-by-step explanation:

First, we can split the shape into 2 rectangles.

This will give us a rectangle with a width of 13 and 10.

Let's work out 1 rectangle at a time.

Area of a rectangle=Width times by legth

13*18=234- This is the area of 1 of the rectangles.

10*14=140- This is the area of the second rectangle

Now we add the areas together to get 374 square millimeters, which is the area of this figure.

the general equation of a graph is given by

y = mx + c

where m= slope

c=intercept

the equation given is

9x-5y=4

make y subject of formula

9x-4=5y

5y=9x-4

divide through by 5

y=9/5x-4/5

comparing with the general equation

mx=9/5x

m=slope=9/5

Answer: H- hot dogs

J- juice box

6h+4j=16.70

3h+4j=10.85

Elimination:

-6h-4j=-16.70

3h+4j=10.85

-3h=-5.85

H= 1.95

3(1.95)+4j=10.85

5.85+4j=10.85

4j=5

J=1.25

1.95 dollars for a hotdog and 1.25 dollars for a juice box

Step-by-step explanation:

Answer:

-$6, $0, and $17

The value of x for the given quadratic expression is x = 5 ± √11.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given expression is 3(x-5)²=33. The value of x will be calculated as,

3(x-5)²=33

(x - 5 )² = 11

(x - 5 )  = ±√11

x = 5 ± √11

Therefore, the value of x for the given quadratic expression is x = 5 ± √11.

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the year-end amount in Justin's account is $6575.44.

How to solve the question?

(a) To write the year-end amount in terms of the original amount, we can use the following formula:

Year-end amount = Original amount - Decrease

Substituting the given values, we get:

Year-end amount = $6600 - $24 = $6576

Now, to express the year-end amount in terms of the original amount, we can divide both sides of the above equation by the original amount:

Year-end amount / Original amount = ($6600 - $24) / $6600

Simplifying this expression, we get:

Year-end amount / Original amount = 0.9964

Therefore, the year-end amount is 0.9964 times the original amount.

(b) Using the answer from part (a), we can determine the year-end amount in Justin's account as follows:

Year-end amount = 0.9964 x $6600

Simplifying this expression, we get:

Year-end amount = $6575.44

Therefore, the year-end amount in Justin's account is $6575.44.

It is worth noting that the decrease of $24 corresponds to a decrease of approximately 0.36% in the original amount. This decrease could be due to various factors, such as market fluctuations or fees associated with the investments account. To better understand the reasons behind the decrease, Justin may want to review the account statement and consult with a financial advisor. Additionally, he may want to reevaluate his investment strategy and consider diversifying his portfolio to mitigate risks and maximize returns.

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The required answers are,

a) 675.75 \(ft^2\)

b) 9.46 gallons or we can say that 10 gallons needed.

c) $183.2

The amount of unit squares that cover a closed figure's surface is its area. Area is measured in square units like cm² and m². Area of a shape is a two dimensional quantity. The term “area” refers to the space inside the boundary or perimeter of a closed shape.

Now in the given question,

Area of Walls:

\(A(walls)=2(11*8)+2(20*8)\\A(walls)=2(88)+2(160)\\A(walls)=176+320\\A(walls)=496 ft^2\)

Area of 2 windows:

\(A(windows)=2(3*4)\\A(windows)=2*12\\A(windows)=24 ft^2\)

Area of door:

\(A(door)=2.5*6.5\\A(door)=16.25 ft^2\)

Area of walls to be painted:

\(=A(walls)-A(windows)-A(door)\\=496-24-16.25\\=455.75ft^2\)

Area of ceiling:

\(A(ceiling)=11*20\\A(ceiling)=220ft^2\)

(a) Now total area to be painted:

A(walls to be painted)+ A(ceiling)=A(total)

\(A(total)=455.75 ft^2+220ft^2\\A(total)=675.75 ft^2\)

(b) Number of Gallons:

coverage=71.41 ft^2 /gallon

675.75 ft^2/71.41 ft^/gal=gallons needed

9.46 gal= 10 gallons needed(approx)

(c) Cost of Paint:

You would need to buy 10 gallons at $18.32/gallon to have sufficient paint

cost=10 gallons x $18.32/gallon

=$183.2

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There are 230230 possible groups.

Each of the different groups or selections can be formed by taking some or all of a number of objects, irrespective of their arrangments is called a combination.

Given that Total employees = 26

The Number of employees want to choose = 6

Tthe combination of m things taken k at a time is given by the following formula:

\(^mC_k = \dfrac{m!}{k! \times (m-k)!}\)

Putting m = 26 and k= 6, we obtain;

C = 230230

Therefore, we can conclude that there are 230230 possible groups.

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Combining both cases, we can conclude that |x² - y³| ≤ |x - pP| holds for all x, y ∈ R and 0 < p < 1. The specific conditions of 1 > p > 0 and the limit of x₁ approaching L are not directly related to the given inequality and do not affect its validity.

Let's analyze the inequality step by step. Starting with |x² - y³| ≤ |x - pP|, we can observe that both sides involve absolute values, which means we need to consider two cases: positive and negative values.

Case 1: x² - y³ ≥ 0

In this case, the absolute value on the left side can be removed without changing the inequality. Thus, we have x² - y³ ≤ |x - pP|.

Case 2: x² - y³ < 0

In this case, we need to consider the negative value and change the sign of the inequality. So, -(x² - y³) ≤ |x - pP|.

Now, let's analyze the right side of the inequality, |x - pP|. Since 0 < p < 1, we know that pP is less than P. Therefore, |x - pP| represents the distance between x and pP, which is smaller than the distance between x and P.

Combining both cases, we can conclude that |x² - y³| ≤ |x - pP| holds for all x, y ∈ R and 0 < p < 1. The specific conditions of 1 > p > 0 and the limit of x₁ approaching L are not directly related to the given inequality and do not affect its validity.

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