If UY= 3x - 6 and YV = x + 2, find UV.

(WY INTERSECTS UV AT Y)

Postulate: AA

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

The dimension of the box should be 1.7×1.7×3.58 in inches, applying minimization of surface area.

Dimensions to Minimize the Surface Area of the Box

It is given that the box is square based with an open top.

⇒ The box has one square and 4 rectangles

Thus, the total surface area of the box is given as,

S= a²+ab+ab+ab+ab  

S= a²+4ab ______________ (1)

Here, a is the side of the squared base and length of the rectangular sides of the box, b is the breath of the rectangular sides of the box.

This equation is later used for minimization of the surface area.

Also, the volume, V = a²b

It is also given that volume of the box is 184 in³.

⇒ 184 = a²b _____________ (2)

Forming a One-Variable Equation

From equation (2), b=184/a²

Now, substitute this value of b in equation (1) to get,

S = a² + 4a(184/a²)

S = a² + 4(184/a)

S = a² + 736/a

Minimization of Surface Area to find the Dimension

We require a dimension that will minimize the surface area of the box. Hence, applying minimization surface area, dS/da = 0

dS/da = 2a -736/a²

0 = 2a -736/a²

⇒ 0 = 2a³- 736

2a³ = 736

a³ = 736/2

a³ = 368

a = ∛368

a= 7.17 in

∵V = a²b

184 = (7.17)²b

b = 184/7.17²

b = 184/51.4089

b = 3.58 in

Therefore, 1.7×1.7×3.58 in inches is the required dimension for the box, using minimization of surface area..

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Answer:

3+10 square root of 2

Step-by-step explanation:

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

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]

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 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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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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Answer: the answer is 661.55

Step-by-step explanation:

interest formula: F = Pe^(rt)

A data value is considered significantly low or significantly high  if its​ z-score is less than -2 or greater than 2.

What does it mean if z-score is 2?

What does a standard deviation of 2 mean?

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The correct question is -

A data value is considered​ _______ if its​ z-score is less than minus−2 or greater than 2.

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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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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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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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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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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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

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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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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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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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.

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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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

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:

2/50=1/25

Step-by-step explanation:

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

Answer: I believe its 50 because you would have to see 3 x what equals 150

Step-by-step explanation:

The time taken to her to bag 150 bags is 50 minutes.

Grocery Items are any of the items listed that are offered only for off-premises consumption are as follows:-

(1) packaged or fresh fish, meat, or poultry.

(2) packaged or fresh plants or vegetables.

(3) packaged or fresh dairy goods (other than ice cream, frozen yogurt, or other confection/dessert items).

According to the given question, Three grocery bags are packed every minute. So, the time taken to 150 bag the time taken is computed as follows:-

Time Taken =  Total number of bags/Number of bags per minute

                   =  150 / 3

                   =  50 minutes

Therefore, it can be concluded that the time taken for her to bag 150 bags is 50 minutes.

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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

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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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 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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