Question 9 of 10
A fellow classmate tosses 3 coins and finds that 2 of them come up tails.
Which of the following is the best conclusion for her to come to?
OA. She needs to keep flipping the coins until she gets 50% heads in
order to determine if they are fair.
OB. If she flips the coins once more, they will all come up heads.
OC. The coins are unfair.
OD. This could easily happen with a fair coin after only 3 flips.

Answer:

X     Y

5      7

20   28

60   84

This table shows the proportional relationship.

Step-by-step explanation:

The equivalent ratios of two variables known as proportional relationship.

Table 1:  X     Y                                        Table 3: X     Y

              4     6                                                       12    5

              8     12                                                      18    7

              18    26                                                     26   9

Ratio = 4:6 = 8:12 ≠ 18:26                       Ratio = 12:5 ≠ 18:7 ≠ 26:9

Table 2: X     Y                                       Table 4: X     Y

              5     7                                                       3      2

              20   28                                                    9      8

              60   84                                                    15     14

Ratio = 5:7 =20:28=60:84                       Ratio = 3:2 ≠ 9:8 ≠ 15:14

Here we see table 2 shows the proportional relationship.

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Answer: [tex]35^{\circ}[/tex]

Step-by-step explanation:

Angles ACB and DCA add to form angle ACB, which is a right angle, so:

So, [tex]m\angle ACB=6(7)-7=\boxed{35^{\circ}}[/tex]

Option third "He could draw a diagram of a rectangle with dimensions x – 1 and x – 6 and then show the area is equivalent to the sum of x², –x, –6x, and 6' is correct.

It is defined as the area occupied by the rectangle in two-dimensional planner geometry.

The area of a rectangle can be calculated using the following formula:

Rectangle area = length x width

We have a quadratic expression to model the area of the rectangle:

= x² – 7x + 6

[tex]\rm =\left(x^2-x\right)+\left(-6x+6\right)[/tex]

[tex]=\rm x\left(x-1\right)-6\left(x-1\right)[/tex]

= (x - 1)(x - 6)

Thus, option third "He could draw a diagram of a rectangle with dimensions x – 1 and x – 6 and then show the area is equivalent to the sum of x², –x, –6x, and 6' is correct.

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Using proportions, it is found that the measure of the inscribed angle B is of 30º.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

In a circle, the inscribed angle is half the measure of the outside angle. Hence, in this problem, the measure of angle B is of 50% of 60º, hence:

m<B = 0.5 x 60º = 30º.

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Answer:

Using proportions, it is found that the measure of the inscribed angle B is of 30º.

Step-by-step explanation:

Each given factor written as a polynomial in descending order is;  (7x + 6y)(49x² - 42xy + 36y²)

We are given the polynomial;

343x³ + 216y³

343x³ + 216y³ is a sum of cubes and factors in general as;

a³ + b³ = (a + b)(a² - ab + b²)

Thus;

343x³ + 216y³ = (7x)³ + (6y)³

= (7x + 6y)((7x)² - 7x(6y) + (6y)² )

= (7x + 6y)(49x² - 42xy + 36y²)

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By the binomial theorem,

[tex]\displaystyle \left(x^2 + \frac px\right)^6 = \sum_{n=0}^6 \binom 6n \left(x^2\right)^n \left(\frac px\right)^{6-n} = \sum_{n=0}^6 p^{6-n} \binom 6n x^{3n-6}[/tex]

where

[tex]\dbinom kn = \dfrac{k!}{n!(k-n)!}[/tex]

is the so-called binomial coefficient.

The term that's independent of x is the constant term, which occurs when [tex]3n-6=0[/tex], or [tex]n=2[/tex]. Given that this constant 240, we have

[tex]p^{6-2} \dbinom62 = 240 \implies p^4 = 16 \implies p = \pm2[/tex]

but [tex]p[/tex] must be positive, so [tex]\boxed{p=2}[/tex]

Answer:

-4/3

Step-by-step explanation:

mtan × mline = -1

mtan× 3/4 = -1

mtan =-4/3

Answer:

$6847.955

Explanation:

Use the compound interest formula, but the value decreases over time.

[tex]\sf A = P(1 - \dfrac{r}{100} )^t[/tex]

where 'A' is final amount, r is rate, t is time

Inserting P = $15,000, r = 23, t = 3 years

[tex]\sf A = 15000(1- \dfrac{23}{100} )^3[/tex]

[tex]\sf A = 6847.995[/tex]

Hence the value of truck after three years will be $6847.955.

Answer:

y = 97°

Explanation:

Opposite angles in a quadrilateral inscribed in a circle sum ups to 180°

So following the rule:

A + C = 180°

y + 83° = 180°

y = 180° - 83°

y = 97°

Answer:

from the image above

Triangle ABE = Triangle ADE

AE = AE ( common).

angle AEB = angle AEO ( each 90°)

AB = AD ( given).

by side angle side criteria

so area of ABE = area of ADE

similarly,

BC = DC ( given)

BEC = DEC ( 90°)

EC = EC ( 9m each)

so area of BEC = Area of DEC

Answer:

1/3×22/7×r^2h

Step-by-step explanation:

the volume =1/3 ×22/7×r^2×13.5

Answer:

[tex]\frac{45}{7}[/tex]

Step-by-step explanation:

9 is the same as [tex]\frac{9}{1}[/tex]

∴ 9 ˣ [tex]\frac{5}{7}[/tex]

=  [tex]\frac{9}{1}[/tex] ˣ  [tex]\frac{5}{7}[/tex]

To multiply two fractions, just multiply their numerators together and their denominators together.

9 x 5 = 45

1 x 7 = 7

∴ [tex]\frac{9}{1}[/tex] ˣ  [tex]\frac{5}{7}[/tex]

  = [tex]\frac{45}{7}[/tex]

Answer:

Step-by-step explanation:

Answer:

2 or 3

Step-by-step explanation:

write it down dummy

Answer:

1.4y

Step-by-step explanation:

T is a linear transformation from R²→R² with basis {(1,0),(0,1)}
T: (x,y)→(x+6,y+4)

A function from one vector space to another that preserves the underlying (linear) structure of each vector space is called a linear transformation.

Then the vector (1,0) goes to (1+6,4)=(7,4)=7(1,0)+4(0,1)

and the vector (0,1) goes to (6,1+4)=(6,5)=6(1,0)+5(0,1)

So, the matrix of the transformation is

[tex]\left[\begin{array}{ccc}7&6\\4&5\end{array}\right][/tex]

The inverse of the matrix is

[tex]\left[\begin{array}{ccc}\frac{5}{11}&\frac{-6}{11}\\ \\\frac{-4}{11}&\frac{7}{11}\end{array}\right][/tex]

So, the Inverse Transformation is given by

[tex]T^{-1}(x,y)=\left[\begin{array}{ccc}\frac{5}{11}&\frac{-6}{11}\\ \\\frac{-4}{11}&\frac{7}{11}\end{array}\right]\left[\begin{array}{ccc}x\\y\end{array}\right] =(\frac{5x-6y}{11}, \frac{-4x+7y}{11})[/tex]

So, no option is correct. And the answer is

[tex]T^{-1}(x,y)=(\frac{5x-6y}{11}, \frac{-4x+7y}{11})[/tex]

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Answer:

B

Step-by-step explanation:

using the addition identity for sine

sin(A + B) = sinAcosB + cosAsinB

using the sine and cosine ratios in the right triangle

sinABC = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{AC}{AB}[/tex] = [tex]\frac{4}{5}[/tex]

cosABC = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{BC}{AB}[/tex] = [tex]\frac{3}{5}[/tex]

using the exact values

sin60° = [tex]\frac{\sqrt{3} }{2}[/tex] , cos60° = [tex]\frac{1}{2}[/tex]

Then

sin(ABC + 60)

= sinABC cos60 + cosABC sin60

= ( [tex]\frac{4}{5}[/tex] × [tex]\frac{1}{2}[/tex] ) + ([tex]\frac{3}{5}[/tex] × [tex]\frac{\sqrt{3} }{2}[/tex] )

= [tex]\frac{4}{10}[/tex] + [tex]\frac{3}{10}[/tex] [tex]\sqrt{3}[/tex]

= [tex]\frac{2}{5}[/tex] + [tex]\frac{3}{10}[/tex] [tex]\sqrt{3}[/tex]

sin<ABc

cos<ABC

Now

Answer:

Question 4: letter c

Question 3: letter c

Step-by-step explanation:

Answer:

Step-by-step explanation:

3x + 2(x − 1) − 4 =

3x + 2x - 2 - 4 =

5x - 6

Answer:

Step-by-step explanation:

[tex]\bf 3x + 2(x - 1) - 4?[/tex]

Distribute.

Subtract the numbers.

Combine like terms.

Answer:

[tex]x = 45 \sqrt{5} [/tex]

Step-by-step explanation:

[tex] {3}^{2 log_{3}(x) + log_{3}(5) } = {3}^{ 4log_{3}(15) } [/tex]

[tex] {3}^{ log_{3}( {x}^{2} ) } {3}^{ log_{3}(5) } = {3}^{ log_{3}( {15}^{4} ) } [/tex]

[tex]5 {x}^{2} = {15}^{4} [/tex]

[tex] {x}^{2} = \frac{ {15}^{4} }{5} [/tex]

[tex]x = \frac{ {15}^{2} }{ \sqrt{5} } ( \frac{ \sqrt{5} }{ \sqrt{5} } )[/tex]

[tex]x = \frac{ {15}^{2} \sqrt{5} }{5} = 45 \sqrt{5} [/tex]

Answer:

-x + 4

Step-by-step explanation:

(4x+5)+(−5x−1)

4x+5−5x−1  [Remove the parentheses]

-x + 4           [Combine Like Terms]

Answer:

-x+4

Step-by-step explanation:

Given:

(4x+5)+(−5x−1)

Solution:

To re-write this in it's simplest terms:

Combine like terms:

Hence the simplest form is -x+4.

Done.

Answer: D

Step-by-step explanation:

We know that the line [tex]y=10[/tex] is shaded below, so it represents [tex]y \leq 10[/tex].

Similarly, the line [tex]y=x+1[/tex] is shaded above, so it represents [tex]y > x+1[/tex].

The 15 are women, keeping track of the number of men chosen is Not binomial the trials are not independent.

We have given that,

The given procedure results in a binomial distribution. If not, state the reason why. Choosing 5 people (without replacement) from a group of 58 people, of which 15 are women, keeping track of the number of men chosen.

In samples with replacement, the probability has to be the same for each trial, that is, they are independent.

Hypergeometric distribution

Samples without replacement, as the probabilities depend on the previous outcomes, that is, they are not independent.

In this question

Marbles are chosen without replacement, which means that for each trial the probabilities of choosing a red marble are different, which means that the trials are not independent. So the answer is:

Not binomial the trials are not independent.

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Answer:

The value of t is 6.65

An exponential function is a mathematical function of the following form: f ( x ) = a^x. where x is a variable, and a is a constant called the base of the function.

Given:

A= 210 million

P= A e^(kt)

225 = 210 * e ^ (0.0069t)

225/210=  e ^ (0.0069t)

1.07 =  e ^ (0.0069t)

Taking log on both side

log  1.047 = 0.0069 t log e

[tex]\frac{0.0069t\ln \left(e\right)}{0.0069\ln \left(e\right)}=\frac{\ln \left(1.047\right)}{0.0069\ln \left(e\right)}[/tex]

t= log ( 1.047) / 0.0069

t= 6.65

Hence, value of t is 6.65.

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Answer:

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

f(x) = x²

f(x) becomes f(13x) + 6

the "+ 6" at the end tells us already everything, because there is only one aber option listed that contains a shift up. and that is exactly what that "+ 6" did. it adds 6 to every possible y value of the function. so, the whole function moves up by 6 units.

and yes, the 13x of f(13x) stretches the function horizontally (along the x axis).

simply said, whenever the x value for the original function increased by 1, it increases for the new function by 13.

Answer:

1/2

Step-by-step explanation:

(Is this the question? In the pic above)

Sin of an angle os the side opposite over it divided by the hypotenuse.

Sin = opposite/hypotenuse

Sin = 5/10

Sin = 1/2