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At an amusement park, the probability that a child eats a hot dog and drinks a soda pop is 0.38. The probability that a child eats a hot dog is 0.61, and the probability that a child drinks soda pop is 0.89. What is the probability (rounded to the nearest hundredth) that a child drinks soda pop given that the child has already eaten a hot dog? Hint: cap p left parenthesis cap a vertical line cap b right parenthesis equals start fraction cap p left parenthesis cap a intersection cap b right parenthesis over cap p left parenthesis cap b right parenthesis end fraction

A| 0.34
B| 0.43
C| 0.62
D| 0.69

The congruence statements that are correct for the given scenario are △GHI ≅ △LMN, △IHG ≅ △NML, and △GIH ≅ △NML.

The correct congruence statements for the given scenario are:

These congruence statements indicate that the corresponding sides and angles of the triangles are equal, leading to overall congruence.

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The term that describes the relationship the three points must have is known as: collinear.

Collinear points are points positioned on a shared straight line, forming a linear arrangement.

In the figure referred to above, we see that point U is on the same straight line as point R and point N. This makes than have a linear arrangement, hence, we can use the term known as collinear to describe the relationship between the three points.

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Answer:

C. 124.3 ft

Step-by-step explanation:

Let h represent Nick's distance from ground.

We have been given that Nick is stuck at the top of a ferris wheel. his mother is standing 38 feet from the base of the wheel watching him. The angle of elevation from nick's mom to nick is 73 degrees.

Nick, his mother and angle of elevation forms a right triangle with respect to ground, where, h is opposite side and 38 feet is adjacent side.

[tex]\text{tan}=\frac{\text{Opposite}}{\text{Hypotenuse}}[/tex]

[tex]\text{tan}(73^{\circ})=\frac{h}{38}[/tex]

[tex]\text{tan}(73^{\circ})*38=\frac{h}{38}*38[/tex]

[tex]3.270852618484*38=h[/tex]

[tex]h=3.270852618484*38[/tex]

[tex]h=124.292399502392[/tex]

[tex]h\approx 124.3[/tex]

Therefore, Nick is 124.3 feet above the ground.

Answer:

$11,840.85

Step-by-step explanation:

y - x > -3

(6, 2) → x = 6, y = 2

substitute

2 - 6 = - 4 < -3 NOT

(2, 6) → x = 2, y = 6

substitute

6 - 2 = 4 > -3 CORRECT

(2, -1) → x = 2, y = -1

substitute

-1 - 2 = -3 NOT

Answer: (2, 6)

Answer:  [tex]x-100[/tex]

Step-by-step explanation:

Given : Phil received a prize of x dollars from a poker tournament.

The tournament cost him 100 dollars to enter.

To find Phil's net winnings from the tournament, we need to subtract the tournament cost from the prize amount he had won.

Thus, the expression to show Phil's net winnings from the tournament :-

[tex]x-100[/tex]

Final answer:

The cyclist will travel approximately 20.17 meters before coming to a complete stop when decelerating with an acceleration of [tex]-3.0 m/s^2[/tex] from an initial speed of 11 m/s.

Explanation:

To calculate the distance the cyclist's bike will travel while coming to a complete stop with an initial speed of 11 m/s and an acceleration of [tex]-3.0 m/s^2[/tex], we can use one of the equations of motion. Specifically, we need to use the equation [tex]v^2 = u2 + 2as[/tex], where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the distance.

In this case, the final velocity v = 0 m/s (because the bike comes to a stop), the initial velocity u = 11 m/s, and the acceleration a = [tex]-3 m/s^2[/tex] (the negative sign indicates that it is a deceleration).

Plugging these values into the equation, we get:

0 = 112 + 2(-3)s

0 = 121 - 6s

6s = 121

s = 121/6

s = 20.17 meters

Thus, the cyclist will travel approximately 20.17 meters before coming to a complete stop.

Answer:

(A)[tex]G(F(x))=(x-5)^2[/tex]

Step-by-step explanation:

Given: It is given that [tex]F(x)=x-5[/tex] and [tex]G(x)=x^2[/tex].

To find: [tex]G(F(x))[/tex]

Solution:

It is given that  [tex]F(x)=x-5[/tex] and [tex]G(x)=x^2[/tex], then [tex]G(F(x))[/tex] is written as:

[tex]G(F(x))=G(x-5)[/tex]

⇒[tex]G(F(x))=(x-5)^2[/tex]

Thus, it matches with the option A of the given options.

The value of expression with the given x and y value is 8/15.

The given expression is -x+4y, -x=-4/5 and y=1/3.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

Now, put x=4/5 and y=1/3 in the given expression and simplify

That is, -4/5 + 4(1/3)

=-4/5 + 4/3

Take LCM of denominators 5 and 3 is 15

Now, -12/15 + 20/15

=(-12+20)/15

=8/15

Therefore, the value of expression with the given x and y value is 8/15.

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The range of this data set will be 8. The range of the data set is simply the difference between the maximum and the minimum value.

A data set is a set of information that corresponds to one or more database tables in the case of tabular data,

The maximum value is 12

The minimum value is 4

The range of  the data set will be;

R = M-m

R=12-4

R=8

Hence the range of this data set will be 8.

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We have a golden rule about similarity of figures. It is "All circle are always similar to each other".

In other words, Every circle is dilated version of another circle. To find the value of dilation, we can find the ratio of its redii.

The ratio of radii of two circles is called the scale factor of dilation between them.

Given are two circles with following information :-

Circle 1: center (0, 9) and radius 14

Circle 2: center (0, 9) and radius 7

Finding the ratio of their radii :-

[tex] \frac{Circle\; 1\; radius}{Circle\; 2\; radius} =\frac{14}{7} = 2 [/tex]

So, scale factor is 2. It means circle 1 is a dilation of circle 2 with a scale factor of 2.

Hence, option A is correct i.e. Circle 1 is a dilation of circle 2 with a scale factor of 2.

Answer:

106.8 in2

Step-by-step explanation:

Answer:  Option (2) is correct.

Step-by-step explanation:

Since we have given that

KLM is a right triangle, in which KM = 15, and ln is an altitude.

As we know that for right angled triangle, there are 3 conditions :

[tex]KL^2=KN.KM-----(1)\\\\ML^2=MN.KM-------(20\\\\LN^2=KN.MN------(3)[/tex]

So, According to the options ,

Put LM = 12, NM = 9,

[tex]\text{Using eq. (3), we have}\\\\LN^2=KM.MN\\\\12^2=9\TIMES 16\\\\144=144[/tex]

Since, it satisfies that KLM is a right triangle.

Hence, Option (2) is correct.

Using Pythagorean theorem, Option D: [tex]\( LM = 8 \)[/tex] and [tex]\( NM = 10 \)[/tex], satisfies [tex]\( KM^2 = LM^2 + NM^2 \)[/tex].

[tex]\( LM = 12 \) and \( NM = 9 \).[/tex]To determine which lengths would make triangle [tex]\(KLM\)[/tex] a right triangle when [tex]\(\overline{LN}\)[/tex] is an altitude and [tex]\(KM = 16\)[/tex], we can use the Pythagorean theorem to check each given set of values. We know that [tex]\(\overline{LN}\)[/tex] divides [tex]\(KLM\)[/tex] into two right triangles, [tex]\( \triangle KNL \)[/tex] and [tex]\(\triangle LNM\)[/tex].

We will check each given option to see if the Pythagorean theorem holds.

Option A: [tex]\( LM = 13 \)[/tex] and [tex]\( KN = 6 \)[/tex]

Here, [tex]\( LN \)[/tex] is the altitude. Let [tex]\( NM = x \)[/tex], then [tex]\( KM = KN + NM \)[/tex], so:

[tex]\[ x = 16 - 6 = 10 \][/tex]

For [tex]\( \triangle LNM \)[/tex]:

[tex]\[ LM^2 = LN^2 + NM^2 \][/tex]

[tex]\[ 13^2 = LN^2 + 10^2 \][/tex]

[tex]\[ 169 = LN^2 + 100 \][/tex]

[tex]\[ LN^2 = 69 \][/tex]

[tex]\[ LN = \sqrt{69} \approx 8.3 \][/tex]

For [tex]\( \triangle KNL \)[/tex]:

[tex]\[ KL^2 = KN^2 + LN^2 \][/tex]

[tex]\[ KL^2 = 6^2 + 69 \][/tex]

[tex]\[ KL^2 = 36 + 69 \][/tex]

[tex]\[ KL^2 = 105 \][/tex]

[tex]\[ KL \approx 10.2 \][/tex]

These calculations do not match the given [tex]\(KL\)[/tex] value.

Option B: [tex]\( LM = 12 \) and \( NM = 9 \)[/tex]

Here, [tex]\( LN \)[/tex] is the altitude. Let [tex]\( KN = x \)[/tex], then:

[tex]\[ x = 16 - 9 = 7 \][/tex]

For [tex]\( \triangle LNM \)[/tex]:

[tex]\[ LM^2 = LN^2 + NM^2 \][/tex]

[tex]\[ 12^2 = LN^2 + 9^2 \][/tex]

[tex]\[ 144 = LN^2 + 81 \][/tex]

[tex]\[ LN^2 = 63 \][/tex]

[tex]\[ LN = \sqrt{63} \approx 7.9 \][/tex]

For [tex]\( \triangle KNL \):[/tex]

[tex]\[ KL^2 = KN^2 + LN^2 \][/tex]

[tex]\[ KL^2 = 7^2 + 63 \][/tex]

[tex]\[ KL^2 = 49 + 63 \][/tex]

[tex]\[ KL^2 = 112 \][/tex]

[tex]\[ KL \approx 10.6 \][/tex]

These calculations do not match the given [tex]\(KL\)[/tex] value.

Option C: [tex]\( KL = 11 \)[/tex] and [tex]\( KN = 7 \)[/tex]

Here, [tex]\( LN \)[/tex] is the altitude. Let [tex]\( NM = x \)[/tex], then:

[tex]\[ x = 16 - 7 = 9 \][/tex]

For [tex]\( \triangle KNL \)[/tex]:

[tex]\[ KL^2 = KN^2 + LN^2 \][/tex]

[tex]\[ 11^2 = 7^2 + LN^2 \][/tex]

[tex]\[ 121 = 49 + LN^2 \][/tex]

[tex]\[ LN^2 = 72 \][/tex]

[tex]\[ LN = \sqrt{72} \approx 8.5 \][/tex]

For [tex]\( \triangle LNM \)[/tex]:

[tex]\[ LM^2 = LN^2 + NM^2 \][/tex]

[tex]\[ LM^2 = 72 + 9^2 \][/tex]

[tex]\[ LM^2 = 72 + 81 \][/tex]

[tex]\[ LM^2 = 153 \][/tex]

[tex]\[ LM \approx 12.4 \][/tex]

These calculations do not match the given [tex]\(LM\)[/tex] value.

Option D: [tex]\( LN = 8 \) and \( NM = 10 \)[/tex]

Here, [tex]\( LN \)[/tex] is the altitude. Let [tex]\( KN = x \)[/tex], then:

[tex]\[ x = 16 - 10 = 6 \][/tex]

For [tex]\( \triangle LNM \)[/tex]:

[tex]\[ LM^2 = LN^2 + NM^2 \][/tex]

[tex]\[ LM^2 = 8^2 + 10^2 \][/tex]

[tex]\[ LM^2 = 64 + 100 \][/tex]

[tex]\[ LM^2 = 164 \][/tex]

[tex]\[ LM \approx 12.8 \][/tex]

For [tex]\( \triangle KNL \)[/tex]:

[tex]\[ KL^2 = KN^2 + LN^2 \][/tex]

[tex]\[ KL^2 = 6^2 + 8^2 \][/tex]

[tex]\[ KL^2 = 36 + 64 \][/tex]

[tex]\[ KL^2 = 100 \][/tex]

[tex]\[ KL = 10 \][/tex]

These calculations match the given lengths.

Thus, the correct answer is:

D. [tex]\( L N = 8 \) and \( N M = 10 \)[/tex]

The correct question is given below:

Answer:

it is 10xyz^3 for monomial. 8x^2+0.25 and -x^2y^2+2y for binomial. And -2x^2-x+3.5 and x^3y^4+2x^2y-3z for trinomial.

Step-by-step explanation:

[tex]10xyz^3[/tex] for monomial.  [tex]8x^2+0.25[/tex] and [tex]-x^2y^2+2y[/tex] for binomial. And [tex]-2x^2-x+3.5[/tex] and [tex]x^3y^4+2x^2y-3z[/tex] for trinomial.

They are mathematical expressions involving variables raised with non negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non negative exponentiation of variables involved.

We need to find each polynomial (monomial, binomial, trinomial) based on number of terms it contains.

Therefore,

If there is one term, the polynomial will be called monomial thus;

[tex]10xyz^3[/tex]

If there are two terms, the polynomial will be called binomial thus;

[tex]8x^2+0.25[/tex] and [tex]-x^2y^2+2y[/tex]

If there are three terms, the polynomial will be called trinomial thus;

[tex]-2x^2-x+3.5[/tex] and [tex]x^3y^4+2x^2y-3z[/tex]

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The numbers between 61 and 100 are given as 80 and 100.

The LCM or least common multiple of two numbers is such a small number that is divisible by both. It can be obtained by taking the prime factors of both the numbers and then taking the product of them having highest power.

The required numbers between 61 and 107 are given as follows,

The LCM of 2,4 and 5 is 20.

Thus, the numbers divisible by 2, 4 and 5 are multiples of 20.

Now, the multiples of 20 are 20, 40, 60, 80 and 100.

80 and 100 lies between 61 and 107.

Hence, the numbers that Ali can choose are given as 80 and 100.

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