What is 2 with an exponent of 0?

Answer:

2/50=1/25

Step-by-step explanation:

2 aces are removed hence 2 aces are left out of 50 cards

Using similar triangles, it is found that the height of the taller pole is of 9.6m.

Similar triangles are triangles that have the same angles, and whose side lengths are proportional.

The hypotenuse of the smaller triangle is given as follows:

h² = 6² + 8² -> h = 10.

Hence the proportional relationship is:

[tex]\frac{10}{16} = \frac{6}{h}[/tex]

Applying cross multiplication:

10h = 96

h = 9.6m.

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If P(a)=0.5 and P(b) =0.45, then P(a ∩ b) is 0.225.

Independent events are events such that the occurrence of one event won't affect the other.

Therefore,

P(a) × P(b) = P(a ∩ b)

Hence,

P(a) = 0.5

P(b) = 0.45

Therefore,

P(a ∩ b) = 0.5 × 0.45

P(a ∩ b) = 0.225

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Answer: Right isosceles triangle

Step-by-step explanation: This is fairly easy to determine.

Side BC is roughly congruent to side CD. Both sides start from 0 to 7 and a little bit.

Side AC is also congruent by the reflexive property and is also congruent to both triangles' sides because it lines up perfectly. Since both sides BC and CD are congruent, the segment AC likely is perpendicular to segment BD and cuts it into 2 equal and congruent sides.

Sides AB and AD cannot be determined to be congruent.

Since the right angles are between two congruent sides of two triangles, the two triangles are congruent by the Side Angle Side congruence theorem.

Thus, we can say these are 2 right isosceles triangles conjoined together. Hope this helped!

(Proof is attached.)

Answer:

A little less than 320

Step-by-step explanation:

Round the miles to 168 and 150

Add together 168 + 150 = 318

Answer: a. a little less than 320

John get money $630 and bill get money $270.

Given that John and bill shared $900 in the ratio 7:3 respectively.

The ratio is defined as the comparison of two quantities of equal units, indicating the quantity of one quantity contained in the other quantity.

The total ratio is 7+3=10

For john:

John has money seven out of 10 for the $900, we get

J=900×(7/10)

J=90×7

J=630

For bill:

Bill is three out of ten for $900, we get

B=900×(3/10)

B=90×3

B=270

Hence, john get money $630 and bill get $270 when they both shared $900 in the ratio 7:3 respectively.

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Answer:

slope: undefined

equation: x = p

y-intercept: there is none

slope of perpendicular: 0

Step-by-step explanation:

points: (p, a), (p, -a)

slope = (-a - a)/(p - p) = -2a/0

The slope is undefined since the line is vertical.

equation: x = p

Since p ≠ 0, the vertical crosses the x-axis at a point that is not x = 0 and never intersects the y-axis, so the is no y-intercept.

A line perpendicular to he given line is a horizontal line.

slope = 0

Answer:

3+10 square root of 2

Step-by-step explanation:

[tex](3 + 10) \sqrt{2} [/tex]

The unknown sides and angles of the triangle are 18 cm and 39 degrees respectively.

The side and angle of a triangle can be found as follows:

using sine law,

Angle A = 180 - 68 - 59 = 53 degrees

19.5 / sin 59 = a / sin 53

19.5 sin 53 = a sin 59

a = 19.5 sin 53 / sin 59

a = 15.5733924459 / 0.8571673007

a = 18.1680280047

a = 18 cm

15 / sin ∅ = 20 / sin 57

15 sin 57 = 20 sin ∅

sin ∅ = 12.5800585192 / 20

sin ∅= 0.62900292595

∅ = sin ⁻¹ 0.62900292595

∅ = 38.9763828249

∅ = 39 degrees.

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By definition of a binomial random variable,  the probability that the machine will be working is 0.82045.

First of all, you should know that the Probability is the greater or lesser possibility that a certain event will occur.

In other words, the probability establishes a relationship between the number of favorable events and the total number of possible events.

On the other hand, a random variable is a function that associates a real number, perfectly defined, to each sample point.

A random variable is discrete if the numbers it gives rise to are integers.

Finally, a binomial distribution is a discrete probability distribution that describes the number of successes in performing n independent experiments on a random variable.

The expression to calculate the binomial distribution is:

P(X=x)=([tex]n\\ x[/tex]) pˣ qⁿ⁻ˣ

Where:

Remember that:

([tex]n\\ x[/tex])=[tex]\frac{n!}{x!(n-x)!}[/tex]

where the exclamation mark represents the factorial symbol, that is, the product of all positive integers from 1 to n.

A machine has 28 identical components which function independently. The probability that a component will fail is 0.19.

The following random variable is defined:

x= the number of components will stop working.

Being n the total number of pieces (in this case, 12 pieces) and p the probability of success (the piece fails, in this case 0.19), the expression to be used is expressed as:

P(X=x)=([tex]12\\ x[/tex]) 0.19ˣ (1-0.19)¹²⁻ˣ

P(X=x)=[tex]\frac{12!}{x!(12-x)!}[/tex] 0.19ˣ (0.81)¹²⁻ˣ

Since the machine will stop working if more than three components fail, you need to know the probability that the machine will be working if 3 or less than 3 components fail. In other words, it may be that 0, 1, 2 or 3 pieces are broken and the machine continues to work:

P(X≤3)= P(X=0) + P(X=1) + P(X=2) + P(X=3)

Then:

P(X≤3)= [tex]\frac{12!}{0!(12-0)!}[/tex] 0.19⁰ (0.81)¹²⁻⁰ + [tex]\frac{12!}{1!(12-1)!}[/tex] 0.19¹ (0.81)¹²⁻¹ + [tex]\frac{12!}{2!(12-2)!}[/tex] 0.19² (0.81)¹²⁻² + [tex]\frac{12!}{3!(12-3)!}[/tex] 0.19³ (0.81)¹²⁻³

Solving:

P(X≤3)= [tex]\frac{12!}{0!12!}[/tex] ×1×(0.81)¹² + [tex]\frac{12!}{1!11!}[/tex] 0.19×(0.81)¹¹ + [tex]\frac{12!}{2!10!}[/tex] 0.19²×(0.81)¹⁰ + [tex]\frac{12!}{3!9!}[/tex] 0.19³×(0.81)⁹

P(X≤3)= 1×1×(0.81)¹² + 12×0.19×(0.81)¹¹ + 66×0.19²×(0.81)¹⁰ + 220×0.19³×(0.81)⁹

P(X≤3)= (0.81)¹² + 2.28×(0.81)¹¹ + 2.3826×(0.81)¹⁰ + 1.50898×(0.81)⁹

P(X≤3)= 0.82045

Finally, the probability that the machine will be working is 0.82045.

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Answer:

Step-by-step explanation:

The visualization of "4.298" on the number line is attached below.

Suppose we're measuring something whose values are numeric.

For each value of that thing we observe, we plot a dot above that value in the number line.

Thus, the total number of dots in the dot plot tells us the total number of observations of the values of that thing we did.

Thus, suppose if we observed the value 'x', then we will make a dot above 'x'. If there is already a dot over 'x', then we will make a new dot over that dot.

We know that 4.298 is greater than 4 but less than 5.

The visualization of "4.298" on the number line is attached below.

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Answer: the answer is 661.55

Step-by-step explanation:

interest formula: F = Pe^(rt)

Step-by-step explanation:

The picture is the full explanation for this question answer.

18.19 is the solution for the given improper function.

The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.

To add 8 11/12 and 9 5/18, we need to first find a common denominator. The smallest number that both 12 and 18 divide evenly is 36.

Converting 8 11/12 to an improper fraction:

8 11/12 = (8 × 12 + 11) / 12 = 107/12

Converting 9 5/18 to an improper fraction:

9 5/18 = (9 × 18 + 5) / 18 = 167/18

Now that we have a common denominator of 36, we can add the two fractions:

107/12 + 167/18 = (107 × 3) / (12 × 3) + (167 × 2) / (18 × 2)

= 321/36 + 334/36 = 655/36

So 8 11/12 + 9 5/18 = 655/36 or approximately 18.19.

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The simplified form of the expression [1/5 (-16-9) + 4² ÷ 8] is -3.

Option A) is the correct answer.

Given the expression;  1/5 (-16-9) + 4² ÷ 8

First we remove the parentheses and perform the operations using the guidelines of BODMAS

1/5 (-16-9) + 4² ÷ 8

1/5 × -25 + 4² ÷ 8

1/5 × -25 + 16 ÷ 8

-25/5 + 16/8

-5 + 2

-3

The simplified form of the expression [1/5 (-16-9) + 4² ÷ 8] is -3.

Option A) is the correct answer.

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It takes 15 hours to drive to Atlanta. Using the distance-time-speed formula the required time is calculated.

The relation between distance 'd', time 't', and speed 's' is given by the formula,

s = d/t or

d = st or

t = d/s

It is given that,

The distance to uncle's house = 444 miles

The time taken to drive to uncle's house = 12 hours

So,

speed = (444)/12 = 37 miles/hour

Then the time to drive 555 miles(to Atlanta) is calculated by,

time t = (555)/37 = 15 hours

Therefore, it takes 15 hours to drive to Atlanta at 555 miles of distance.

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Answer:

180

Step-by-step explanation:

Solution 1: Any straight line is 180 degrees.

Solution 2: Angle WX=Angle YZW+ Angle YZX

Angle YZW=Angle YZX=90

Angle YZW+ Angle YZX=90+90=180

So Angle WX=180

Answer:

Step-by-step explanation:

You can find WX if you know some special properties of special triangles:

1. A 45-45-90 triangle (a triangle with angle measures of 45°, 45°, and 90°) will have a 1:1:√2 ratio (the legs of the triangle are the same length and the hypotenuse is the length of any leg times √2)

2. A 30-60-90 triangle (a triangle with angle measures of 30°, 60°, and 90°) will have a 1:√3:2 ratio (the hypotenuse is twice the measure of the shorter leg, and the longer leg is √3 times the length of the shorter leg)

For reference, a leg is a side on a right triangle that isn't the hypotenuse.

In this picture, the first type of triangle is on the right, and the second type is on the left.

The shorter leg on the left triangle has a length of 10, and WZ is the longer leg. The longer leg is √3 times the shorter one, so WZ = 10√3

Both legs of a 45-45-90 triangle have the same measure, so ZX is 10.

Since WX is made up of WZ and ZX, it's length is the sum of both lengths.

[tex]{\rm WX} = 10\sqrt{3}+10[/tex]

[tex]{\rm WX} \approx 27.321[/tex]

Answer:

20

Step-by-step explanation:

so we need to see that

3/4 x ? = 15

so we say

3 x ? = 15x4

? =60/3

?= 20

The number of credit hours a student have to take for the two tuition costs to be equal is 2.5 hours. Option A

c(h) = 250 + 200h

s(h) = 300 + 180h

Where,

To have equal tuition in both schools,

equate both function

250 + 200h = 300 + 180h

200h - 180h = 300 - 250

20h = 50

h = 50/20

h = 2.5 hours.

The number of credit hours a student have to take for the two tuition costs to be equal is 2.5 hours.

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The answer is D.

The formula to find area of a circle is : πr²

Here, we are given the diameter, but we need the radius. Always remember that the radius is always half the diameter.

Let's find the area.

The two methods which can be used to solve the quadratic equation are; The completing the square method and the factor method.

Although, not limited to the aforementioned methods of solving quadratic equations, the two methods are major methods of solving quadratic equations.

The completing the square method (also used in expressing quadratic equations in vertex form) and the factor method are very efficient method of solving quadratic equations.

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Postulate: AA

Similarity statement: [tex]\triangle CBA \sim \triangle FED[/tex]

The angle of the given ray is of x = 150º.

The angle of the ray is given by the sum of the angles that compose the ray.

In this problem, the angles are of 65º, 40º and 45º, hence:

x = 65 + 40 + 45 = 150º

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Therefore, the 500th term of the sequence exists 3517.

The given sequence is 24, 31, 38, 45, 52, ...

It exists an Arithmetic progression.

Here, the First term = 24

Common difference = 31 - 24 = 7

The given explicit formula for the nth term exists

an = a₁ + (n - 1)d

Where a₁ exists the first term, d exists a common difference.

Substitute a₁ = 24, d = 7 and n = 500

a(500) = 24 + (500 - 1)7

 = 24 + (499)7

 = 24 + 3493

a(500) = 3517

Therefore, the 500th term of the sequence exists 3517.

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To solve a triangle means to obtain al the missing parts of the triangle.

To solve a triangle means to obtain al the missing parts of the triangle. Now we have the following information;

<ABC = 51°

c = 8

a = 11

Then;

b^2 = a^2 + c^2 - 2acCos B

b^2 = (11)^2 + (8)^2 - [2 * 11 * 8 * cos 51]

b^2 = 121 + 64 - 55.38

b = 11.39

Now;

a/sinA = b/sinB

asinB = bsinA

sinA = asinB/b

sinA = 11 * sin 51/11.39

A = 48.6 or 49°

C = 180 - (49 + 51)

C = 80°

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The value of [tex]x \sim B (10, 0.75)[/tex] for x = 5 is 0.06

The expression is given as:

[tex]x \sim B (10, 0.75)[/tex]

This means that:

n = 10

p = 0.75

The probability is then calculated as

[tex]P(x)= ^nC_x * p^x *(1 - p)^{n-x[/tex]

This gives

[tex]P(5)= ^{10}C_5 * 0.75^5 *(1 - 0.75)^5[/tex]

Evaluate the combination expression

[tex]P(5)= 252 * 0.75^5 *0.25^5[/tex]

Evaluate

P(5)= 0.06

Hence, the value of [tex]x \sim B (10, 0.75)[/tex] for x = 5 is 0.06

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Considering that it is a triangle, the range of the possible lengths, x, of the third side of the tile is: (1, 17).

In a triangle, the sum of the lengths of the two smaller sides has to be greater than the length of the greater side.

Hence, if 9 is the greater side:

8 + x > 9

x > 1.

If 8 and 9 are the smaller sides:

x < 8 + 9

x < 17.

Hence the range of possible lengths is:

(1, 17).

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Answer:

27.183, 27.2

Step-by-step explanation:

First, do the formula for the triangle:

[tex]\frac{1}{2}[/tex] x 4.1 x 2.6 = 5.33

Next, multiply that by the base side:

5.33 x 5.1 = 27.183

Answer:

1/2 x 4.1 x 2.6 = 5.33

5.33 x 5.1 = 27.183

Rounding off to nearest tenth = 27.2 m^3

The three consecutive integers are 5, 6, and 7.

What are consecutive integers?

Whole numbers that follow one another without a gap are known as consecutive integers. A few examples of consecutive integers are 15, 16, and 17, 1,2 and 3, and so on.

Finding the Consecutive Integers

Let the three consecutive integers be a, a + 1, and a + 2.

These three consecutive integers are to be such that two times the first integer when added to three times the second integer minus the third integer, it is equal to 21.

⇒ 2a + 3(a+1) - (a+2) = 21

2a + 3a + 3 - a -2 = 21

5a - a + 3 - 2 = 21

4a + 1 = 21

4a = 20

a = 20/4

a = 5

∴ a+1 = 5+1

a+1 = 6

And, a+2 = 5 + 2

a +2 =7

Hence, the three consecutive integers come out to be 5, 6, and 7

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Using linear functions, the cost will be the same, of $70, when there are 5 students.

A linear function is modeled by:

y = mx + b

In which:

In this problem, the functions are:

The costs are the same when:

45 + 5x = 35 + 7x

2x = 10

x = 5.

The cost is:

y = 45 + 5 x 5 = $70.

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