A rectangular gate is made using 6 straight pieces of steel.
5 m
12 m
The weight of the steel is 2.5 kg per metre.
+
Work out the total weight of the steel gate.
Pythagoras' Theorem - A Simple Approach View One Minute Version
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11.
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Answer:

463×10³

463×1000

=0.463

9514 1404 393

Answer:

Step-by-step explanation:

Plot the given points on the graph. Those that are on the (solid) boundary line or in the shaded area are solutions. Those in the white space are not solutions.

Answer:

won't it make 30 smoothies

Step-by-step explanation:

then that means danielle makes more!!

As per the given box plot, on 6th day island is more likely to have a wind speed close to its median.

The term box plot in math referred as the method of  visually show the distribution of numerical data and skewness through displaying the data quartiles and averages.

Here we have given the figure attached that contains the box plots show the average wind speeds, in miles per hour, for two different islands Here the Country A is placed on the top of the line where as Country B on the bottom of the line.

While we looking into the box plot we have identified that the median of Country A is 4 and the center of the box is 5

And the the median of Country B is 6 and the center of the box is 6.5.

Through this we have identified that the resulting day is 6 day.

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The volume of the prism, in cubic units is 1/2x³ + x²

The volume of the oblique prism is given as:

V = Base area * Height

Given the following

Base area = 1/2 (x*x)

Base area = 1/2 x²

Get the volume of the prism;

Volume of the prism = 1/2(x²)(x+2)

Volume of the prism = 1/2(x³+2x²)

Volume of the prism = 1/2x³ + 1/2(2x²)

Volume of the prism = 1/2x³ + x²

Hence the volume of the prism, in cubic units is 1/2x³ + x²

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Answer:

1/2x³ + x²

Step-by-step explanation:

edg

Answer:

for store a 260 + 20 times x and then store b 140 + 30 times x

Step-by-step explanation:

We have the next function

First, we need to calculate the derivate of the function

the critical points are when the derivate is 0 or can be calculated

in this case, x=-5 is a critical point and it doesn't belong

to the interval given therefore the number of critical points is 0

Answer:

0.328571 km per minute

Step-by-step explanation:

The measure of the obtuse angle in the triangle is 108 degrees.

A triangle is a polygon with three sides. The total sum of the angles in a triangle is 180 degrees.

Therefore, the measure of the obtuse angle in the triangle can be found as follows;

An obtuse angle is an angle which is greater than 90° and less than 180°.

Hence, the angles of the triangle are 1x, 3x and 6x.

3x + 1x + 6x = 180

10x = 180

x = 180 / 10

x = 18

Therefore, the obtuse angle of the triangle is 6(18) = 108 degrees.

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Answer:

c) 108 on edgen

If a researcher were to subtract the mean of a distribution from each score in that distribution and add the differences, the resulting value would always be zero.

Explanation:

When the mean of a distribution is subtracted from each score, it effectively centers the distribution around zero. This is because subtracting the mean from each score removes the average distance from the mean, making the new mean equal to zero. Consequently, when the differences are added, the positive and negative deviations cancel each other out, resulting in a sum of zero.

Mathematically, if we have a set of scores \($\{x_1, x_2, x_3, ..., x_n\}$\) and their mean is denoted as \($\mu$\), the process can be represented as:

\($$(x_1 - \mu) + (x_2 - \mu) + (x_3 - \mu) + ... + (x_n - \mu) = 0$$\)

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The  examples that would constitute a discrete random variable are;

I. Total number of points scored in a football game

III. Number of near collisions of aircraft in a year

A discrete random variable has only a countable number of different values that it can assume. Usually, but not always, discrete random variables are counts. A random variable is discrete if it can only take a finite number of different values. A variable whose value is determined by counting is referred to as a discrete variable.

A continuous variable is one whose value may be determined through measurement. A random variable is a variable whose value is the resultant number of an unpredictable event.

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As a result of Charles investing both locally and internationally, C.  If one market fails to perform, the other market may continue to provide returns

When Charles invested in both local and international stock, he engaged in a process known as diversification.

Diversification reduces risk because there is a chance that when some stock are not performing well, others will be because they are not affected by the same things.

Charles's stock will not be affected by the same things such that when the domestic stock isn't doing well, the international stocks might be doing well.

In conclusion, option C is correct.

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Answer:

Select the correct answer.

Charles is planning to buy both domestic and international stock to add to his portfolio. What benefit will he gain from including both kinds of investments?

A.

His investments in the international market will be affected if his domestic stocks don’t perform well.

B.

High exchange rates in the international market will boost his domestic investments.

C.

If one market fails to perform, the other market may continue to provide returns.

D.

The domestic stocks will make the currency exchange rate among international stocks easier to manage.

Step-by-step explanation:

The first step is to find out how much more food the Seniors collected than the Sophomores. We know that they collected two and a half times more, which is the same as 2.5 times 125 = 312.5 pounds of food.

Therefore, the Seniors collected 312.5 pounds of food.

The angle that the line 3y = 2x + 6 makes with the [x] axis is (θ) = 33°69'.

Given is the equation -

3y = 2x + 6

The given equation is -

3y = 2x + 6

y = (2/3)x + (6/3)

y = (2/3)x + 2

Slope of the line -

m = 2/3.

We know slope is also given by -

m = tan(θ)

So -

tan(θ) = 2/3

(θ) = tan⁻¹(2/3)

(θ) = 33°69'

Therefore, the angle that the line makes with the [x] axis is (θ) = 33°69'.

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Answer:

no solution

Step-by-step explanation:

3x + 4y = 6

3x + 4y = 5

=> slope is same but y-intercept will be different

=> they will not intersect

=> no solution

Answer:

no solutions

Step-by-step explanation:

3x + 4y = 6 → (1)

- 3x - 4y = - 5 → (2)

add the 2 equations term by term

0 + 0 = 1

0 = 1 ← false statement

This indicates the system has no solution

Answer:

D.

Step-by-step explanation:

350-150 is 200.

Multiply that by 4.

Answer is four times as much as 200!

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The point- slope form of the line is y-5 = -0.25(x+6).

What is line?

A line is an one-dimensional figure. It has length but no width. A line can be made of a set of points which is extended in opposite directions to infinity. There are straight line, horizontal, vertical lines or may be parallel lines perpendicular lines etc.

A line with a slope of –1/4 passes through the point (–6,5)

Any line in point - slope form can be written as

y - y₁= m(x -x₁) -------(1)

where,

y= y coordinate of second point

y₁ = y coordinate of first point

m= slope of the line

x= x coordinate of second point

x₁ = x coordinate of first point

In the given problem (x₁ , y₁) = (-6,5) and m= -1/4

Putting all these values in equation (1) we get,

y-5= (-1/4) (x- (-6))

⇒ y-5 = -0.25(x+6)

Hence, the point- slope form of the line is y-5 = -0.25(x+6).

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Solving a system of equations we will see that the two numbers are:

4 - √384*i and 4 + √384*i.

We want to find two numbers x and y such that the product is 400 and the sum is 8, then we can write a system of equations:

x*y = 400

x + y = 8

Let's isolate x on the second equation to geT:

x = 8 - y

And replace that in the first equation to get:

(8 - y)*y = 400

8y - y² = 400

Now we have the quadratic equation:

-y²  + 8y - 400 = 0

Using the quadratic formula we will get:

\(y = \frac{-8 \pm \sqrt{8^2 - 4*(-1)*-400} }{2*-1} \\\\y = \frac{-8 \pm \sqrt{-1,536} }{-2} \\\\y = 4 \pm \sqrt{384}i\)

So there are two possible values of y.

if we take the first one, then:

y = 4 + √384*i

In this case the value of x will be:

x = 8 - y = 8 - (4 + √384*i) =  4 - √384*i

We got the other value for x.

So the two numbers are  4 - √384*i and 4 + √384*i.

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The function is an exponential function because the y values increase by an equal factor over equal intervals of x-values.

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

At point (1, 9):

9 = ab¹

At point (2, 36):

36 = ab²

b = 4, a = 2.25

y = 2.25(4)ˣ

The function is an exponential function because the y values increase by an equal factor over equal intervals of x-values.

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Answer:

40

Step-by-step explanation:

Total is 150

Germany=1/3 *150 = 50

Italian= 2/5 * 150 = 60

Total - Germany- Italian= French

150 - 50 -60= 40

The probability that all four strawberry pieces will be received by the same child 9/10 outcome.

Total piece of candy = 40

Mint flavor = 36

Strawberry = 04

There are 36 + 04 = 40 total outcomes for the chocolate pick.

There are 36 outcomes resulting in you picking a mint candy.

Probability is the number of outcomes you’re testing for divided by the number of total outcomes. So in this case that’s 36/40 or 4/5 . And also,  

04 /40 = 1/10

Therefore, adding both, we get,

4/5 + 1/10 = 9/10

The probability that all four strawberry pieces will be received by the same child is 9/10.

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Answer:

82 degrees

Step-by-step explanation:

It should all equal 180 so 52+46=98 and 180-98 is 82

The equilibrium price of the product is $10 at a quantity of 10 items.

To find the equilibrium price and quantity, we need to set the quantity demanded equal to the quantity supplied:

QD = QS

30 - 2p = 5 + 3p

Solving for p, we get:

5p = 25

p = 5

So the equilibrium price is $5.

To find the equilibrium quantity, we substitute p = 5 into either the demand or supply equation. Using the demand equation:

QD = 30 - 2(5) = 20

So the equilibrium quantity is 20.

Therefore, the equilibrium price of the product is $10 at a quantity of 10 items.

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Answer: x = -51/4 or -12 3/4

Step-by-step explanation:

\(\begin{array}{l}\frac{2}{5}\left(\frac{x-1}{2}\right)=-2\frac{3}{4}\\\\\frac{2}{5}\left(\frac{x-1}{2}\right)=-\frac{11}{4}\\\\5\cdot\frac{2}{5}\cdot\frac{x-1}{2}=5\left(-\frac{11}{4}\right)\\\\x-1=-\frac{55}{4}\\\\x-1+1=-\frac{55}{4}+1\\\\x=-\frac{51}{4}\ or\ -12\ \frac{3}{4}\end{array}\)

Answers to Question 6: m∠1 = 92, m∠2 = 88

    The sum of a linear pair's angles is 180°, so we will set up an equation to solve.

(x + 67) + (3x + 13) = 180

4x + 80 = 180

4x = 100

x = 25

    -

(x + 67) ➜ (25 + 67) ➜ 92

(3x + 13) ➜ (3(25) + 13) ➜ 88

Answer to Question 7: m∠2 = 56

    Vertical angles are congruent, or equal, so we can set up an equation to solve.

(5x + 16) = (4x + 24)

x = 8

    -

(5x + 16) ➜ (5(8) + 16) ➜ 56

(4x + 24) ➜ (4(8) + 24) ➜ 56

The given function f(x) = 25e^(-2x) represent the exponential decay.

According to th egiven question.

We have an exponential function.

f(x) = 25e^(-2x)

As we know that

If \(P = P_{o} e^{-kt}\) be an exponential function, then it will represent

Where,

P is the final amount

\(P_{o}\) is the intial amount

t is the time interval

k is the constant of proportionality

For the given question if we compare the given exponential function with the standard exponentential function we get

\(P_{o}\) = 25

k = 2

and t = x

Now,

e^(-2) = 0.13

Since, e^(-2) < 1.

Hence, the given function f(x) = 25e^(-2x) represent the exponential decay.

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Answer:

(2x-³y⁴)³(x³+y⁰)÷(4xy-²)³

Its 2.3 per year and the question says 2 years ago so 2.3×2

=4.6%

So,

210 000÷100×4.6

=9660

now

9660+210000

=219 660

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