Round £432.75
to 2 significant
figure.

The required probabilities are \(P(\text{pennies})=\dfrac{13}{28},P(\text{nickels})=\dfrac{27}{140},P(\text{dimes})=\dfrac{3}{14},P(\text{quarters})=\dfrac{9}{70}\).

Given:

Pennies = 65

Nickels = 27

Dimes = 30

Quarters = 18

To find:

The probability of each.

Solution:

The probability formula:

\(\text{Probability}=\dfrac{\text{Favorable outcome}}{\text{Total outcomes}}\)

Total number of coins:

\(65+27+30+18=140\)

The probability of selecting Pennies is:

\(P(\text{pennies})=\dfrac{65}{140}\)

\(P(\text{pennies})=\dfrac{13}{28}\)

The probability of selecting nickels is:

\(P(\text{nickels})=\dfrac{27}{140}\)

The probability of selecting dimes is:

\(P(\text{dimes})=\dfrac{30}{140}\)

\(P(\text{dimes})=\dfrac{3}{14}\)

The probability of selecting quarters is:

\(P(\text{quarters})=\dfrac{18}{140}\)

\(P(\text{quarters})=\dfrac{9}{70}\)

Therefore, the required probabilities are \(P(\text{pennies})=\dfrac{13}{28},P(\text{nickels})=\dfrac{27}{140},P(\text{dimes})=\dfrac{3}{14},P(\text{quarters})=\dfrac{9}{70}\).

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Answer:

ASA

Step-by-step explanation:

As we know that the Two corresponding angles are equal along with their Included Side (Side bounded by the angles) are equal as they share the common Included Side, through ASA criterion we can prove that the two angles are congruent.

The correct answer is option A. 14 ÷ (5 + c).

Barry exists spreading the cards among the suits, then he needs enough suits to hold the total of 14 cards he has. Hence, we need to divide the total number of cards by the total number of cards,

An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.

A number, a variable, or a mix of numbers, variables, and operation symbols make up an expression. Two expressions joined by an equal sign form an equation.

If we assume Barry exists spreading the cards among the suits, then he needs enough suits to hold the total of 14 cards he has. Hence, we need to divide the total number of cards by the total number of cards.

Therefore, the correct answer is option A. 14 ÷ (5 + c)

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Answer:

sqrt(68) is the length.

Step-by-step explanation:

For this you will use the distance formula, sqrt((x2-x1)^2+(y2-y1)^2)

So for this it is sqrt((5+3)^2+(-2+4)^2)

sqrt(64+4)

sqrt(68)

8.246

Answer:

Multiply x by 5 and 2 by 5

Step-by-step explanation:

The answers are worded very badly, but if you look closely you can get rid of most of them just because it's not possible to do yet:

So the first step would be bubble two just from getting rid of your other choices.

Answer:

6 line segments can be drawn

Answer:

  H)  6

Step-by-step explanation:

You want to know the number of line segments that can be drawn between 4 noncollinear points.

The number of possible segments is the number of unique pairs of points.

4 points can be chosen 2 at a time in (4·3/2) = 6 ways.

There are 6 possible line segments that can be drawn between these points.

__

Additional comment

The number of combinations of k items from a field of n items is given by ...

  nCk = n!/(k!(n-k)!)

For line segments, k=2, so this becomes (n)(n-1)/2.

The six (6) line segments are the four (4) around the outside to form a quadrilateral, and the two (2) across the middle that are the diagonals of that quadrilateral.

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The statement that completes the two column proof is:

Statement 4: ∠ACE ≅ ∠BCD

Two column proof is the most common formal proof in elementary geometry courses. Known or derived propositions are written in the left column, and the reason why each proposition is known or valid is written in the adjacent right column.  

The two column proof is as follows:

Statement 1. AE ⊥ EC;BD ⊥ DC

Reason 1. given

Statement 2. ∠AEC is a rt. ∠; ∠BDC is a rt. ∠

Reason 2. definition of perpendicular

Statement3. ∠AEC ≅ ∠BDC

Reason 3. all right angles are congruent

Statement 4. ?

Reason 4. reflexive property

Statement 5. △AEC ~ △BDC

Reason 5. AA similarity

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Answer:

(a - b)/(a + b).

Step-by-step explanation:

a²-ab-ac+bc / a² +ab-ac-bc

= a(a - b) - c(a - b) / a(a + b) - c(a + b)

= (a - c)(a - b) / (a - c)(a + b)

The (a - c) is common to top and bottom, so

= (a - b)/(a + b).

Answer:

C. 3

Step-by-step explanation:

One of the (many) properties of definite integrals is
\(\mbox{\large \int\limits _{a}^{b}f(x)\,dx + \int\limits _{b}^{c}f(x)\,dx = \int\limits }_{a}^{c}f(x)\,dx\)

Therefore
\(\mbox{\large \int\limits _{-2}^{5}f(x)\,dx + \int\limits _{5}^{2}f(x)\,dx = \int\limits }_{-2}^{2}f(x)\,dx\)

Given

\(\mbox{\large \int\limits _{-2}^{5}f(x)\,dx = 11}}}\para\)

and

\(\mbox{\large \int\limits _{-2}^{2}f(x)\,dx = 14}}\)

We get

\(\mbox{\large 11+ \int\limits _{5}^{2}f(x)\,dx} = 14\)

Subtracting 11 from both sides we get

\(\mbox{\large \int\limits _{5}^{2}f(x)\,dx} = 14 - 11 = 3\\\)

Answer: Choice C which is 3

In summary, the relation R is reflexive, symmetric, antisymmetric, and transitive.

The relation R defined on the set of ordered pairs in A x A by (a, b)R(c, d) whenever a = c or b = d has the following properties:

Reflexive: The relation R is reflexive if for every element (a, b) in A x A, (a, b) R (a, b). In this case, since a = a and b = b, (a, b) R (a, b) holds true for all elements in A x A, making R reflexive.

Symmetric: The relation R is symmetric if for every (a, b) and (c, d) in A x A, if (a, b) R (c, d), then (c, d) R (a, b). In this case, if a = c or b = d, then c = a or d = b, satisfying the condition for symmetry. Therefore, R is symmetric.

Antisymmetric: The relation R is antisymmetric if for every distinct (a, b) and (c, d) in A x A, if (a, b) R (c, d) and (c, d) R (a, b), then (a, b) = (c, d). In this case, if either a = c or b = d, and also c = a or d = b, then it implies that (a, b) = (c, d), satisfying the condition for antisymmetry. Therefore, R is antisymmetric.

Transitive: The relation R is transitive if for every (a, b), (c, d), and (e, f) in A x A, if (a, b) R (c, d) and (c, d) R (e, f), then (a, b) R (e, f). In this case, if either a = c or b = d, and also c = e or d = f, then it implies that either a = e or b = f, satisfying the condition for transitivity. Therefore, R is transitive.

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Answer:

51.85

Step-by-step explanation:

hope this helps lol

51.85

Percentage Calculator: 28 is what percent of 54? = 51.85.

Answer:

x=5

Step-by-step explanation:

x^2+25-10x = x^2-25

-x^2               -x^2

25-10x = -25

-25        -25

-10x = -50

x=5

lets check

(5-5)^2 = 5^2-25

0^2 = 25-25

0 = 0

Answer:

x = 5

Step-by-step explanation:

(x - 5)^2 = (x - 5) (x - 5) =

x^2 -10x + 25 = x^2 - 25

x^2 - x^2 - 10x + 25 = - 25 (x^2 - x^2 = 0)

- 10x + 25 = - 25

- 10x = - 25 - 25

x = - 50/- 10

x = 5

In a proportional relationship between two quantities, the constant of proportionality, often denoted by the letter "k," represents the value that relates the two quantities. The equation y = kx is the standard form for expressing a proportional relationship, where "y" and "x" are the variables representing the two quantities.

Here's a breakdown of the components in the equation:

y: Represents the dependent variable, which is the quantity that depends on the other variable. It is usually the output or the variable being measured.

x: Represents the independent variable, which is the quantity that determines or influences the other variable. It is typically the input or the variable being controlled.

k: Represents the constant of proportionality. It indicates the ratio between the values of y and x. For any given value of x, multiplying it by k will give you the corresponding value of y.

The constant of proportionality, k, is specific to the particular proportional relationship being considered. It remains constant as long as the relationship between x and y remains proportional. If the relationship is linear, k also represents the slope of the line.

For example, if we have a proportional relationship between the distance traveled, y, and the time taken, x, with a constant of proportionality, k = 60 (representing 60 miles per hour), the equation would be y = 60x. This equation implies that for each unit increase in x (in hours), y (in miles) will increase by 60 units.

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Answer:

wouldn't it be -3 * 8 = -24

Step-by-step explanation:

also I love your pfp

Answer:

8

Step-by-step explanation:

-24/-3 = 8

(a) If f(x) is a convex function with x ∈ ℝⁿ, then all local minima of f(x) are also global minima. In other words, if there exists a point xo such that f(x) ≥ f(xo) for all x in a neighborhood of xo, then f(x) ≥ f(xo) for all x ∈ ℝⁿ.

(b) A graph of a non-convex function can be visualized to understand why the statement in part (a) is not true. It will show a scenario where a local minimum is not a global minimum.

(a) To prove that all local minima of a convex function are also global minima, we can utilize the property of convexity. Suppose there is a point xo such that f(x) ≥ f(xo) for all x in a neighborhood of xo. We assume that xo is a local minimum. Now, consider any arbitrary point x in ℝⁿ. We can express x as a convex combination of xo and another point y in the neighborhood, using the convexity property: x = λxo + (1 - λ)y, where λ is a scalar between 0 and 1. Using this expression, we can apply the convexity property of f(x) to get f(x) ≤ λf(xo) + (1 - λ)f(y). Since f(x) ≥ f(xo) for all x in the neighborhood, we have f(y) ≥ f(xo). Therefore, f(x) ≤ λf(xo) + (1 - λ)f(y) ≤ λf(xo) + (1 - λ)f(xo) = f(xo). This inequality holds for all λ between 0 and 1, implying that f(x) ≥ f(xo) for all x ∈ ℝⁿ, making xo a global minimum.

(b) A graph of a non-convex function can demonstrate a scenario where the statement in part (a) is not true. In such a graph, there may exist multiple local minima, but one or more of these local minima are not global minima. The non-convex nature of the function allows for the presence of multiple valleys and peaks, where one of the valleys may contain a local minimum that is not the overall lowest point on the graph. This occurs because the function may have other regions where the values are lower than the local minimum in consideration. By visually observing the graph, it becomes apparent that there are points outside the neighbourhood of the local minimum that have lower function values, violating the condition for a global minimum.

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Answer:

8n+7

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

Answer:

Pythagorean Theorem : a²+b²=c²

a²+38²=42² => a²=1764+1444 => a²=3,208 inch => a=√3,208

=> a=56.64 inch

Step-by-step explanation:

The statement provides two quantities, A and B, expressed as ratios of positive integers c and d. The relationship between the quantities A and B cannot be determined from the information given.

The statement provides two quantities, A and B, expressed as ratios of positive integers c and d. However, no specific values or constraints are given for c and d. Without knowing the specific values or any relationship between c and d, it is impossible to determine the relationship between A and B.

The relative magnitudes of A and B will depend on the values of c and d. If the value of c is greater than d, then A would be greater than B. Conversely, if the value of d is greater than c, then B would be greater than A. However, without any information about the values of c and d or any relationship between them, we cannot determine the relationship between A and B.

Therefore, based on the given information, the relationship between quantities A and B cannot be determined.

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410/5 = ?

410/5 = 82

82 miles per hour

82*12 = ?

82*12 = 984

Answer: 984 miles in 12 hours

Answer:

x=8

Step-by-step explanation:

When you solved for x in #16, you were looking for the value of x to see what x would make both angles congruent since they were alternate interior angles. The same solution x=8, is the solution to #17 when the two lines will intersect.

If you graph both lines they will intersect at x=8.

Answer:

480

Step-by-step explanation:

\(80*6\) = 480

Answer:

She will travel 480 miles in 6 hours

Step-by-step explanation:

All you need to do is Multiply 80 by 6 to get an answer of 480.

Hope that helps!

Answer:

12 cm

Step-by-step explanation:

Length of AD in the given figure is 12 cm

Answer:

which has two solutions: x=-10.35 and 1.35.

Step-by-step explanation:

x = 5/4   or   x = 15/4

Step-by-step explanation:

Two linear equations in two variables can be solved using the substitution techniques, graphical method or by the elimination method.

Let us consider any two real world linear equations in two variables.

x - y = 0

x + y = 4

Now let us first solve them by substitution method:

equation 1 can be written as : x = y ,

Now we substitute this value of x in the second equation:

x + y = 4

or,  y + y = 4

or, 2y = 4

or, y = 2

At x = 2 , y = 2. Hence the solution is (2,2)

Now let us solve by elimination method:

adding equation 1 and 2 we get:

x - y = 0

x + y = 4

2x = 4

or, x =2

at x=2 , y = 4-2 =2 Hence the solution is (2,2)

Now we will solve the equations graphical method.

In the graph attached below we can clearly see that the straight line representation of the two equations intersect at the point (2,2)

Hence the solution is (2,2) .

Therefore any linear equation in 2 variables can be solved by substitution , elimination and graphically.

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Answer: A

Step-by-step explanation:

Corresponding parts of congruent figures are congruent.

The true statement about the paralleogram ABCD and parallelogram EFGH is-

A. ∠C≅∠G

angle C is congruent to angle G

Parallelograms is a quadrilateral that has two pairs of parallel sides and the opposite angles are equal.

Now the given parallelograms are ABCD and EFGH

If AB, BC, CD and DA are the sides in parallelogram ABCD

and ∠A, ∠B, ∠C and ∠D are angles in parallelogram ABCD

Similarly,

EF, FG, GH and HE are the sides in parallelogram EFGH

and ∠E, ∠F, ∠G and ∠H are angles in parallelogram EFGH

Then by congruency we know that,

The opposite sides are parallel and congruent

Hence,

AB≅EF

BC≅FG

CD≅GH

AD≅EH

Similary, The opposite angles are equal

∠ A ≅ ∠ E

∠ B ≅ ∠ F

∠ C ≅ ∠ G

∠ D ≅ ∠ H

Hence, from the given statements we conclude that only true statement is -

A. ∠C≅∠G angle C is congruent to angle G

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Answer:

Step-by-step explanation:

b) Figure 1 is 2² = 4 (which is also 2x2=4 or if you count all the squares = 4)

Figure 2 is 3² = 9 (which is also 3x3=9 or if you count all the squares = 9 )

Figure 3 is 4² = 16 (which is also 4x4=16 or if you count all the squares = 16 )

Figure 4 is 5² =25(which is also 5x5=25 or if you count all the squares = 25)

Figure 5 is 6² = 36(which is also 6x6=36 or if you count all the squares =36)

c) Figure 1 add squares in a horizontal row which is your x-coordinate (2)

then add squares in a vertical row which is your y-coordinate (2)

so (x,y) = (2,2). Graph those points. Do the same for each and your line is a diagonal straight line traveling diagonally upward equally.

f) Equation: a² = a x a

Answer:

Y= -1/3 |x+3| +5

Step-by-step explanation:

An absolute value will always make a V line.

In your particular problem it wants you to reflect it over the x axis, and to do this you simply need to place a negative.

A negative in the beginning of the problem is only there to say whether you flip your line or not, and this means you don't have to worry about it any more.

What it looks like so far: Y= -

Next it wants you to compress the line vertically by 1/3

A number that causes your line to compress is always less than one

A number that stretches your line would be 1 or more

This number is always placed right next to the left of the parenthesis or absolute value.

What it looks like so far: Y= - 1/3

Now we want the line to move left 3 units.

We are now inside of the absolute value because this is where we move the line left or right. This can get a little confusing, but once you get it then you don't forget it.

Inside the line.. a -# moves right and a +# moves left.

This number should be placed inside the absolute value and to the right of the x.

What it should look like: Y= - 1/3 |x + 3|

Now they want us to move the line up by 5 points.

To the outer right side of the absolute value is where we move things up or down.

To move a number up you need to place a + sign with however many places it wants you to move to the right of the sign, but to move the line down you need to place a - sign with however many places it wants you to move to the right of the sign.

To move this up you simply need to place a +5 to the outer right side of the absolute value.

What you should end up with: Y= - 1/3 |x+3| +5