The table shows the results of an experiment in which the spinner shown above was spun 50 times. Find the experimental probability of each outcome.
not shaded

Given:

Consider the given function:

[tex]f(x)=\dfrac{b\cdot(x-a)}{b-a}+\dfrac{a\cdot(x-b)}{a-b}[/tex]

To prove:

[tex]f(a)+f(b)=f(a+b)[/tex]

Solution:

We have,

[tex]f(x)=\dfrac{b\cdot(x-a)}{b-a}+\dfrac{a\cdot (x-b)}{a-b}[/tex]

Substituting [tex]x=a[/tex], we get

[tex]f(a)=\dfrac{b\cdot(a-a)}{b-a}+\dfrac{a\cdot (a-b)}{a-b}[/tex]

[tex]f(a)=\dfrac{b\cdot 0}{b-a}+\dfrac{a}{1}[/tex]

[tex]f(a)=0+a[/tex]

[tex]f(a)=a[/tex]

Substituting [tex]x=b[/tex], we get

[tex]f(b)=\dfrac{b\cdot(b-a)}{b-a}+\dfrac{a\cdot (b-b)}{a-b}[/tex]

[tex]f(b)=\dfrac{b}{1}+\dfrac{a\cdot 0}{a-b}[/tex]

[tex]f(b)=b+0[/tex]

[tex]f(b)=b[/tex]

Substituting [tex]x=a+b[/tex], we get

[tex]f(a+b)=\dfrac{b\cdot(a+b-a)}{b-a}+\dfrac{a\cdot (a+b-b)}{a-b}[/tex]

[tex]f(a+b)=\dfrac{b\cdot (b)}{b-a}+\dfrac{a\cdot (a)}{-(b-a)}[/tex]

[tex]f(a+b)=\dfrac{b^2}{b-a}-\dfrac{a^2}{b-a}[/tex]

[tex]f(a+b)=\dfrac{b^2-a^2}{b-a}[/tex]

Using the algebraic formula, we get

[tex]f(a+b)=\dfrac{(b-a)(b+a)}{b-a}[/tex]          [tex][\because b^2-a^2=(b-a)(b+a)][/tex]

[tex]f(a+b)=b+a[/tex]

[tex]f(a+b)=a+b[/tex]               [Commutative property of addition]

Now,

[tex]LHS=f(a)+f(b)[/tex]

[tex]LHS=a+b[/tex]

[tex]LHS=f(a+b)[/tex]

[tex]LHS=RHS[/tex]

Hence proved.

Answer:

C. Right

Step-by-step explanation:

Hi there!

Perpendicular lines always create right angles when they intersect each other. This is what makes them perpendicular. Therefore, the perpendicular bisector forms a right angle with the line segment.

I hope this helps!

Answer:

6.41667

Step-by-step explanation:

Answer:

I think 6.4

Step-by-step explanation:

hope it's help

The solution is:

The figure has 4 lines of symmetry.

- A vertical line through the middle of the figure.

- A horizontal line through the middle of the figure.

- The two diagonals through the figure are lines of symmetry too.

In mathematics, reflection symmetry, line symmetry, mirror symmetry, or mirror-image symmetry is symmetry with respect to a reflection. That is, a figure which does not change upon undergoing a reflection has reflectional symmetry. In 2D there is a line/axis of symmetry, in 3D a plane of symmetry.

here, we have,

Explanation

Lines of symmetry refer to lines that can be drawn on figures and the figure on either sides of the line will be mirror images of each other.

For example, for this figure given, if a vertical line is drawn straight through the middle of the figure, the two resulting figures on either sides of the vertical line will be mirror images of each other.

So, the other lines of symmetry for this include

- A horizontal line through the middle of the figure

- The two diagonals through the figure are lines of symmetry too.

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Answer:

Karim had 130 chocolates left.

Step-by-step explanation:

The quick way to do this is to notice that if he gave away 35% of his chocolates, he must have 65% left. That comes about by doing

100% (which is what he started with) - 35% = 65%

65% of 200            Change 65% into a fraction

65/100 * 200          Multiply 200 * 65

13000 / 100            Divide by 100

130

Answer:

130 left

Step-by-step explanation:

35% of 200 chocolates is equal to 70 chocolates.

200-70=130 chocolates

Answer:

a=g/q2+m

Step-by-step explanation:Let's solve for a.

ma+q2a=g

Step 1: Factor out variable a.

a(q2+m)=g

Step 2: Divide both sides by q^2+m.

a(q2+m)

q2+m

=

g

q2+m

a=

g

q2+m

_________

#LetsStudy

Using grammatical signals in developing patterns of ideas can be like a zipper because it zips our ideas or combined some information.

Grammatical signals are writing devices that serve to maintain text coherence. The short story is one of the written mediums where we can find these signals.

Important's of Grammatical signals

Grammatical signals are important because they signal relationships between sentences using backreference through the use of pronominal forms, determiners, repetition of keywords, synonyms, and superordination.

In short, they signal the relationship between new sentences and the one before them and they are also important writing devices in text construction.

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Answer:X=-9

Step-by-sep explanation:

4-2X=22

Move towards

⇒-2X=22-4

Multiply -1

⇒2X=-18

Divide by two

⇒X=-9

Answer: razon de ser

Step-by-step explanation:

Tu eres como agua Clara que lluvi del suelo

Answer:

Auto Credit Express, Carvana, Capital one auto loan

Answer and Step-by-step explanation:

10 + 12s would be the algebraic expression.

Because 10 is being added to the product of 12 and s, meaning 12 and s multiply each other.

#teamtrees #PAW (Plant And Water)

9514 1404 393

Answer:

  (0, 2, 6, 7)

Step-by-step explanation:

The range is the list of 2nd numbers in the ordered pairs:

  (0, 2, 6, 7)

Answer:

Por lo tanto, el área de la fórmula de trapecio se da como: Área de un trapecio, A = h (a + b) / 2 unidades cuadradas. "h" es la altitud o altura. Sea a y b la longitud de los lados paralelos de un trapecio ABCD, como a es la longitud de la base y b es la longitud del lado paralelo a a.

Step-by-step explanation:

Answer

its A

Step-by-step explanation:

The length of PQ is perpendicular to RS. The correct option is A.

Geometry is one of the oldest branches of mathematics, along with arithmetic. It is concerned with spatial properties such as figure distance, shape, size, and relative position.

Two geometric objects are perpendicular in elementary geometry if they intersect at a right angle. The perpendicular symbol can be used to represent the condition of perpendicularity graphically. It can be defined between two lines, a line and a plane, or two planes.

Given that the PO and RS intersect to form four right angles. If PO and RS intersect to form four right angles, the side PQ should be perpendicular to the side RS.

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Answer:

x=x

Step-by-step explanation:

Given:

The given sets are:

[tex]U=\{x|x\in N\text{ and }x<10\}[/tex]

[tex]A=\{x|x\text{ is an odd natural number and }x<10\}[/tex]

[tex]B=\{x|x\text{ is an even natural number and }x<10\}[/tex]

[tex]C=\{x|x\in N\text{ and }3<x<5\}[/tex]

To find

The set [tex]B\cap U[/tex].

Solution:

We have,

[tex]U=\{x|x\in N\text{ and }x<10\}[/tex]

[tex]U=\{1,2,3,4,5,6,7,8,9\}[/tex]

[tex]B=\{x|x\text{ is an even natural number and }x<10\}[/tex]

[tex]B=\{2,4,6,8\}[/tex]

Now, [tex]B\cap U[/tex] is the set that contains all the common elements of both sets B and U.

[tex]B\cap U=\{2,4,6,8\}[/tex]

[tex]B\cap U=B[/tex]

Therefore, the correct option is A.

Answer:

Radius ≈ 7 yd

Step-by-step explanation:

Height = 10

Volume = 1540

Missing radius

Use the formula and work backwards

Formula : πr²h

Plug in the given info:

1540 = 3.14 * r² * 10

Work backwards:

1540/10 = 3.14 * r²

154 = 3.14 * r²

154/3.14 = r²

49.044 = r²

√49.044 ≈ 7

Radius = 7

If my answer is incorrect, pls correct me!

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Answer:

The closest measurement is 15.7

Step-by-step explanation:

The formula for circumference is [tex]2\pi r[/tex]

The diameter is double the radius, so to get the radius we divide by 2.

5 divided by 2 is 2.5

Knowing "r" is 2.5 we can plug that into our equation and solve.

2 · [tex]\pi[/tex] · 2.5 ≈ 15.71

The closest measurement is 15.7

Answer: The equation is 2n = 2

Answer:

The probability that a household in Maryland has an annual income of X or more is 1 subtracted by the p-value of [tex]Z = \frac{X - \mu}{\sigma}[/tex], in which [tex]\mu[/tex] is the mean income and [tex]\sigma[/tex] is the standard deviation of incomes.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

In this question:

Mean [tex]\mu[/tex], standard deviation [tex]\sigma[/tex]

What is the probability that a household in Maryland has an annual income of X or more?

The probability that a household in Maryland has an annual income of X or more is 1 subtracted by the p-value of [tex]Z = \frac{X - \mu}{\sigma}[/tex], in which [tex]\mu[/tex] is the mean income and [tex]\sigma[/tex] is the standard deviation of incomes.

Answer:

Height = 10 yd

Step-by-step explanation:

GIVEN :-

TO FIND :-

GENERAL FORMULAE TO BE USED IN THIS QUESTION :-

For a triangle with base 'b' & height 'h' , its area = [tex]\frac{1}{2} \times b \times h[/tex]

SOLUTION :-

[tex]Area = \frac{1}{2} \times Base \times Height[/tex]

[tex]=> 32 = \frac{6.4h}{2}[/tex]

[tex]=> 6.4h = 32 \times 2 = 64[/tex]

[tex]=> h = \frac{64}{6.4} = 10\: yd[/tex]

Answer:

they are just diffrent varibless of numbers

Step-by-step explanation:

Answer:

30

Step-by-step explanation:

.2(24 + L) = L

.48 + .2L = L

.48 = .8L

6 = L

24 + 6 = 30

Answer:

please make the drawings cleared

The exact value of cos(13π/8) is 1/2 [tex]\sqrt{2-\sqrt{2} }[/tex].

Trigonometriic ratios are the ratios of the sides of a right angled triangle. sin , cos, tan, sec, cosec, cot are some of the trigonometric ratios. Sin is the ratio of perpendicular and hypotenuse, cos is the ratio if base and hypotenuse, tan is the ratio of perpendicular and base, secant is the ratio of hypotenuse and base, cosecant is the ratio of hypotenuse and perpendicular, cot is the ratio of base and perpendicular.

We have to find the value of cos (13π/8).

We have to use formula which is following:

cos[tex]Θ[/tex]=[tex]\sqrt{1/2(1+cos 2Θ}[/tex]

=[tex]\sqrt{1/2(1+cos(2*13 π/8)}[/tex]   (π=[tex]π[/tex])

=[tex]\sqrt{1/2(1+cos(3 π+π/4)}[/tex]

=[tex]\sqrt{1/2(1-cos(π/4)}[/tex]

=[tex]\sqrt{1/2(1-1/\sqrt{2} }[/tex]

=[tex]\sqrt{\sqrt{2}-1/2\sqrt{2} }[/tex]

=1/2[tex]\sqrt{2-\sqrt{2} }[/tex]

Hence the value of cos (13π/8) is [tex]1/2\sqrt{2-\sqrt{2} }[/tex].

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Answer:

Width = 108 cm

Step-by-step explanation:

Perimeter =  2 x (length + width)

297 = 2 x (length + width)

148.5 = Length + width

Ratio of Length to Width = 3 : 8

Sum of ratio = 11

[tex]Length = \frac{3}{11} \times 148.5 = 40.5 \ cm\\\\Width = \frac{8}{11} \times 148.5 = 108 \ cm[/tex]

Answer:

Answer is in picture

Step-by-step explanation:

Hope it is helpful...

Answer:

A' (2,-1) B' (4.-1) C' (1,-4)

Step-by-step explanation:

Answer:

(-2,-1)

Step-by-step explanation: