If R is a relation from a set A to the set B and S is a relation from B to C, then the relation SoR
A. is from C to A
B. does not exist
C. is from A to C
D. None of these

A Henry company makes iron balls with radius 6 make approximately 150 balls out of the given amount of iron.

The number of balls Henry can make,  to determine the volume of each ball and then divide the total amount of iron by the volume of a single ball.

The volume of a sphere is given by the formula: V = (4/3) × π ×r²3, where V represents the volume and r is the radius.

Given that the radius is 6 inches and pi (π) is 3.14, substitute these values into the formula to calculate the volume of a single ball:

V = (4/3) × 3.14 × 6²3

= (4/3) ×3.14 × 216

= 904.32 cubic inches

Now, the number of balls by dividing the total amount of iron by the volume of a single ball:

Number of balls = Total iron / Volume of a single ball

= 135648 / 904.32

=150

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The income you need to afford a $425,000 house is largely dependent on your debt-to-income ratio, credit score, and down payment. However, a general rule of thumb is to have an annual income that is at least three times the purchase price of the home, which in this case would be $1,275,000.

To more accurately determine the income needed to afford a $425,000 house, consider factors such as the interest rate on the mortgage, property taxes, homeowners insurance, and any homeowner association fees.

These additional expenses can significantly impact your monthly mortgage payment and thus your income requirements.
It's important to keep in mind that lenders have varying criteria when determining mortgage eligibility and income requirements, so it's best to speak with a mortgage professional to get a more accurate estimate based on your individual circumstances.

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Answer:

all 3 options are true : A, B, C

Step-by-step explanation:

warning : it has come to my attention that some testing systems have an incorrect answer stored as right answer for this problem.

they say that A and C are correct.

but I am going to show you that if A and C are correct, then also B must be correct.

therefore, my given answer above is the actual correct answer (no matter what the test systems say).

originally the information about the alignment of the point F in relation to point E was missing.

therefore, I considered both options :

1. F is on the same vertical line as E.

2. F is not on the same vertical line as E.

because of optical reasons (and the - incomplete - expected correct answers of A and C confirm that) I used the 1. assumption for the provided answer :

the vertical line of EF is like a mirror between the left and the right half of the picture.

A is mirrored across the vertical line resulting in B. and vice versa.

the same for C and D.

this leads to the effect that all 3 given congruence relationships are true.

if we consider assumption 2, none of the 3 answer options could be true.

but if the assumptions are true, then all 3 options have to be true.

now, for the "why" :

remember what congruence means :

both shapes, after turning and rotating, can be laid on top of each other, and nothing "sticks out", they are covering each other perfectly.

for that to be possible, both shapes must have the same basic structure (like number of sides and vertices), both shapes must have the same side lengths and also equally sized angles.

so, when EF is a mirror, then each side is an exact copy of the other, just left/right being turned.

therefore, yes absolutely, CAD is congruent with CBD. and ACB is congruent to ADB.

but do you notice something ?

both mentioned triangles on the left side contain the side AC, and both triangles in the right side contain the side BD.

now, if the triangles are congruent, that means that each of the 3 sides must have an equally long corresponding side in the other triangle.

therefore, AC must be equal to BD.

and that means that AC is congruent to BD.

because lines have no other congruent criteria - only the lengths must be identical.

A numerical expression that matches this diagram is: 7 + 5 = 12

The plus sign represents addition and the equal sign means that the result of the addition is 12.

It is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator.

The diagram 7+5 represents the addition of the numbers 7 and 5. The plus sign represents addition and the equal sign means that the result of the addition is 12.

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Answer: eggplant, Garlic, Brussels sprouts, Kale, Green peas, Swiss chard.

Step-by-step explanation:

Divide los numeros

14/2 = 7

Fraccion equivalente

14/2 = 28/4

Multiplica denominador y numerador por 2.

Answer: (

20

,

38

]

Step-by-step explanation:

(20,38]

Using the trigonometry ratio to find the remaining missing legs of the triangle, the approximate length of the wood needed is: A. 14.2 ft.

The length of the wood needed to trim the window is the perimeter of the triangular shape shown in the image.

To find the perimeter, use the trigonometry ratio, to find the other two legs of the right triangle.

Thus:

Reference angle = 30°

Hypotenuse = 6 ft

Opposite = ?

Apply SOH:

sin 30 = opp/hyp

sin 30 = opp/6

Opp. = sin 30 × 6

Opp. = 3 ft

Find the other leg:

Reference angle = 30°

Hypotenuse = 6 ft

Adjacent = ?

Apply CAH:

cos 30 = adj/hyp

cos 30 = adj/6

Adj. = cos 30 × 6

Adj. = 5.2 ft

Perimeter of the triangle = 5.2 + 3 + 6 = 14.2 ft.

therefore, using the trigonometry ratio to find the remaining missing legs of the triangle, the approximate length of the wood needed is: A. 14.2 ft.

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Answer:

Step-by-step explanation:

Using the trigonometry ratio to find the remaining missing legs of the triangle, the approximate length of the wood needed is: A. 14.2 ft.

Trigonometry Ratios

The length of the wood needed to trim the window is the perimeter of the triangular shape shown in the image.

To find the perimeter, use the trigonometry ratio, to find the other two legs of the right triangle.

Thus:

Reference angle = 30°

Hypotenuse = 6 ft

Opposite = ?

Apply SOH:

sin 30 = opp/hyp

sin 30 = opp/6

Opp. = sin 30 × 6

Opp. = 3 ft

Find the other leg:

Reference angle = 30°

Hypotenuse = 6 ft

Adjacent = ?

Apply CAH:

cos 30 = adj/hyp

cos 30 = adj/6

Adj. = cos 30 × 6

Adj. = 5.2 ft

Perimeter of the triangle = 5.2 + 3 + 6 = 14.2 ft.

therefore, using the trigonometry ratio to find the remaining missing legs of the triangle, the approximate length of the wood needed is: A. 14.2 ft.

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Answer: The diagram shows a rectangle.

Step-by-step explanation:

A rectangle Expression for "a": a = 12b - 30,Expression for "b": b = (12b² - 30b) / (12b - 30),Length of the rectangle: Length = a = 12b - 30,Perimeter of the rectangle: Perimeter = 2 × (13b - 30)

Let's break down the given information step by step:

The area of the rectangle is given as 12b² - 30b.

The expression for "a":

The area of a rectangle is equal to its length (a) multiplied by its width (b). So, set up the following equation:

Area = Length ×Width

12b² - 30b = a × b

To find the expression for "a," divide both sides of the equation by "b":

a = (12b² - 30b) / b

Simplify the expression for "a":

a = 12b - 30

The expression for "b":

From the same equation as above,  that:

Area = Length × Width

12b² - 30b = a × b

To find the expression for "b," divide both sides of the equation by "a":

b = (12b² - 30b) / a

Substitute the value of "a" from the previous expression:

b = (12b² - 30b) / (12b - 30)

The length of the rectangle:

The length of the rectangle is represented by "a," so the expression for the length is: a = 12b - 30

The perimeter of the rectangle:

The perimeter of a rectangle is given by the formula: Perimeter = 2 ×(Length + Width)

Since the rectangle has two pairs of equal sides (opposite sides are equal in a rectangle), the expression for the perimeter will be:

Perimeter = 2 × (a + b)

Substitute the value of "a" from the expression we found earlier:

Perimeter = 2 × ((12b - 30) + b)

Simplify the expression for the perimeter:

Perimeter = 2 ×(13b - 30)

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Step-by-step explanation:

\(30 + 4x + 2 = 80\)

\(4x + 32 = 80\)

\(4x = 48\)

\(x = 12\)

Therefore, the answer is x = 12.

Hoped this helped.

\(BrainiacUser1357\)

Answer

3, the number is 3

Step-by-step explanation:

work backwards, do 8-5 to get three. you can check to see if you're right by adding 5 to 3, which gives you 8.

Answer:

x

=

−

8

−

√

13

3

,

−

8

+

√

13

3

I dont know why the answer is spacing out like this

Answer:

  (-2/21)√21

Step-by-step explanation:

You want the exact value of tan(arccsc(-5/2)).

We know that csc(x) = 1/sin(x), so the angle that has a csc of -5/2 will have a sin of -2/5. This means the expression can be written as ...

  tan(arcsin(-2/5))

Further, we can use tan=sin/cos to rewrite this as ...

  tan(arccsc(-5/2)) = sin(arcsin(-2/5))/cos(arcsin(-2/5))

  = (-2/5)/cos(arcsin(-2/5))

The cosine is found from the identity ...

  cos(x) = √(1 -sin(x)²)

  cos(arcsin(-2/5)) = √(1 -(-2/5)²) = (√21)/5

Using this value in the above expression, we get ...

  tan(arccsc(-5/2)) = (-2/5)/((√21)/5) = -2/√21

  tan(arccsc(-5/2)) = (-2/21)√21 . . . . . . . . . . rationalize the denominator

__

Additional comment

A good calculator can provide a head start. This one (in the first attachment) likes to leave the radical in the denominator, as it gives a more compact expression.

The second attachment shows the square of the answer using the cosecant function. This is to demonstrate the equivalence we claimed above.

The exact values of these things are often irrational square roots, so we checked that possibility by squaring the decimal result. That gave a fraction that tells us the exact value is -√(4/21) = (-2/21)√21.

Graph of the given function f(x) = ( 1 / 3 )x + 1 and g ( x ) = f ( 6x ) is attached for the different values of x and y.  Graph of both the function f(x) and g(x) intersect at point ( 0, 1 ).

As given in the question,

Given function are as follow:

f(x) = ( 1 / 3 )x + 1

g ( x ) = f ( 6x )

Calculate the function g(x) for f ( 6x ) is given by,

g ( x ) = f ( 6x )

⇒ g ( x ) = ( 1 / 3 )6x + 1

⇒ g ( x ) = 2x + 1

Substitute the value of x to get value of f ( x ) and g ( x ) and put it on graph.

After putting all the values of f(x) and g(x) .

Graph intersect at ( 0, 1 )

Graph is attached.

Therefore, graph of the given function f(x) = ( 1 / 3 )x + 1 and g ( x ) = f (6x ) is attached for the different values of x and y.  Graph of both the function f(x) and g(x) intersect at point ( 0, 1 ).

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Answer:

Ddddddddddddddddddddddddd

two because there is 11 people in total and you have two 4 person groups so that would leave 3 people left and you cant make a 4 person group w 3 people

Combination is a way of arranging the required items from a collection of items where the order of selection is not relevant.

If in a jail cell, there are 5 Democrats and 6 Republicans, the possible ways to form a group of 4 is 330.

The number of possible groups is 330.

Combination is a way of arranging the required items from a collection of items where the order of selection is not relevant.

It is given as:

\(^nC_r = \frac{n!}{r!(n-r)!}\)

We have,

The total number of people:

5 Democrats and 6 Republicans = 5 + 6 = 11.

The number of persons in a group = 4.

The number of groups possible are:

= \(^{11}C_4\)

= 11! / 4! ( 11-4)!

= 11! / 4! 7!

= 11 x 10 x 9 x 8 / 4 x 3 x 2

= 330

Thus,

The number of possible groups is 330.

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Answer:

The graphs of the equations 4x - y = 6 and x + y = 4 intersect at  the point whose coordinates are (2,2)

Step-by-step explanation:

The graphs of the equations 4x - y = 6 and x + y = 4 intersect at  the point whose coordinates are?

We need to find the values of x and y by solving the system of equations.

The values of x and y are the point of intersection of those lines.

We have:

\(4x - y = 6--eq(1) \\x + y = 4--eq(2)\)

Adding both equations and finding value of x

\(4x - y = 6\\ x + y = 4\\-----\\5x+0y=10\\5x=10\\x=\frac{10}{5}\\x=2\)

We get, the value of x: x=2

Now, putting value of x in equation 2 to find value of y:

\(x+y=4\\Put\:x=2\\2+y=4\\y=4-2\\y=2\)

So, we get y=2

Therefore we get x=2 and y=2

The solution set is: (2,2)

So, The graphs of the equations 4x - y = 6 and x + y = 4 intersect at  the point whose coordinates are (2,2)

Using the slope and y-intercept, the linear relationship is y = 512x

To find the equation of the linear relationship, we can proceed to use the formula of equation of a straight line. This is given as y = mx + c

The equation of a straight line is given as y = mx + c

Taking two points from the table;

(2, 512) and (15, 3840)

m = y₂ - y₁ / x₂ - x₁

m = 3840 - 512 / 15 - 2

m = 256

Using the slope to find the y - intercept;

y = mx + c

512 = 256(2) + c

512 = 512 + c

c = 512 - 512

c = 0

The equation of line is y = 512x

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The radius of the spherical part is 3 inches and the length of the tube is 21 cm.

The capacity of a cylinder, which determines how much material it can hold, is determined by the cylinder's volume. There is a formula for the volume of a cylinder that is used in geometry to determine how much of any quantity, whether liquid or solid, can be immersed in it uniformly.

Given that the volume when the water is fully dipped is 4554 / 7 cm³. The volume when the length is 9 cm empty is 396 cm³.

The two equations can be formed as below:-

4554 / 7 = πr²l + (2/3)πr³

396 = πr²( l - 9 ) + (2/3)πr³

Subtract the second equation from the first,

( 4554 / 7 ) - 396 = 9πr²

9πr² = 254.5

r² = 9

r = 3 cm

The length will be calculated as:-

4554 / 7 = πr²l + (2/3)πr³

4554 / 7 = π( 3 )²l + (2/3)π(3)³

l = 21 cm

Therefore, the tube's length is 21 cm, and the spherical part's radius is 3 inches.

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The value of u is 38.

To find the value of u, we first need to calculate the sum of all the values in the range of X.

1 + 2 + 3 + 6 + u = 12 + u

Since each value is equally likely, we can calculate the expected value of X using the formula:

E(X) = (1/5) * (1 + 2 + 3 + 6 + u) = (12 + u)/5

We know that the mean of X is 10, so we can set the expected value equal to 10 and solve for u:

(12 + u)/5 = 10

12 + u = 50

u = 38

Therefore, the value of u is 38.

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Answer:

336

Step-by-step explanation:

12*28

Answer:

keeping in mind that 21 months is more than a year, since there are 12 months in a year,  then 21 months is really 21/12 years.

Step-by-step explanation:

(picture)

so, clearly, you can see who's greater.

Check the picture below, so the parabola looks more or less like so, with a vertex at (0 , -7), let's recall the vertex is half-way between the focus point and the directrix.

so this horizontal parabola opens up to the left-hand-side, meaning that the "P" distance is a negative value.

\(\textit{horizontal parabola vertex form with focus point distance} \\\\ 4p(x- h)=(y- k)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h+p,k)}\qquad \stackrel{directrix}{x=h-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{"p"~is~negative}{op ens~\supset}\qquad \stackrel{"p"~is~positive}{op ens~\subset} \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}\)

\(\begin{cases} h=0\\ k=-7\\ p=-9 \end{cases}\implies 4(-9)(x-0)~~ = ~~[y-(-7)]^2 \\\\\\ -36x=(y+7)^2\implies x=-\cfrac{1}{36}(y+7)^2\)

The z-score is -0.933 and the interpretation is that Andy's score is -0.933 standard deviations away from the mean.

From the question, the given parameters about the distribution are

Mean value of the set of data = 100

Standard deviation value of the set of data = 15

The actual data value = 86

The z-score of the data value is calculated using the following formula

z = (Actual data - mean value)/standard deviation

Substitute the given parameters in the above equation

z = (86 - 100)/15

Evaluate the difference

z = -14/15

Evaluate the quotient

z = -0.933

This means that the score is -0.933 standard deviations away from the mean.

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Complete question

The Wechsler IQ test is normally distributed with mean 100 points and standard deviation 15 points.

Andy Warhol was found to have an IQ of 86 on the Wechsler IQ test. What was his z-score and what does that mean in context?

Answer:

Hello!!

The x and y intercepts on the following graph is...

(a) x-intercept \(1\)

(b) y-intercept \(-4\)

Hope this helps!!

EXPLANATION

The division is equal to:

First we need to write the problem in long division format:

8.0 /_ 9.92

Divide 9 by 8 to get 1:

1

8.0 /_ 9.92

Multiply the quotient digit (1) by the divisor 8:

1

8.0 /_ 9.92

8

Subtract 8 from 9:

1

8.0 /_ 9.92

8

1

Add a decimal point to the solution

Bring down the next number of the dividend

1.

8.0 /_ 9.92

8

19

When a researcher uses the Pearson product-moment correlation, two highly correlated variables will appear on a scatter diagram as a tightly clustered group of points that form a linear pattern.

The scatter diagram is a visual representation of the correlation between two variables, where one variable is plotted on the x-axis, and the other variable is plotted on the y-axis. If the two variables have a high positive correlation, then the points on the scatter diagram will form a cluster that slopes upwards to the right.

On the other hand, if the two variables have a high negative correlation, then the points will form a cluster that slopes downwards to the right. The tighter the cluster of points, the higher the correlation between the variables.

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By applying Pythagoras' theorem, the length of x is equal to 10 units.

In Mathematics and Geometry, Pythagorean's theorem is modeled or represented by the following mathematical equation (formula):

x² + y² = z²

Where:

x, y, and z represents the length of sides or side lengths of any right-angled triangle.

Based on the information provided about the side lengths of this right-angled triangle, we have the following equation:

x² = y² + z²

x² = 8² + 6²

x² = 64 + 36

x = √100

x = 10 units.

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