5. Find Y.
Trapezoid Worksheet
Identify Which kind of trapezoid

Answer:

$600

Step-by-step explanation:

We Know

1kg of rice costs $1.20

How much is 500kg?

We Take

1.20 x 500 = $600

So, 500kg of rice cost $600

The calculated area of the plane figure is 467.61 sq ft

From the question, we have the following parameters that can be used in our computation:

The plane figure

The plane figure is a trapezoid

So, we start by calculating the height of the trapezoid as follows (using the pythagorean theorem)

h^2 = 18^2 - (33 - 25)^2

Evaluate

h^2 = 260

So, we have

h = √260

The area of the plane figure is then calculated as

Area = 1/2 * Sum of parallel sides * Height

So, we have

Area = 1/2 * (33 + 25) * √260

Evaluate

Area = 467.61

Hence, the area is 467.61 sq ft

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When we solve the system of equation, we notice that the small candles cost $10 and the large candles cost $15 each.

The system of equation, presented by the table can be expressed as;

12s + 16l = $360

7s + 22l = $400

Lets use the elimination method

(12s + 16l = 360) × 7

(7s + 22l = 400) × 12

The new equation becomes

84s + 112l = 2520

84s + 264l = 4800

We subtract the equation. E2 - E1

(84s + 264l) - (84s + 112l) = 4800 - 2520

(84 - 84) - (264l - 112l) = 2280

152l = 2280

l = 15

Since we know the price of the large candle, we can find the small candle

12s + 16l = 360

12s + 16($15) = 360

12s + 240 = 360

12s = 360 - 240

12s = 120

s = 10

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The range of possible values for the expression -2a + b is -3 ≤ -2a + b ≤ -1.

.Given the inequalities 3 < a < 5 and 5 < b < 7, we need to find all possible values of the expression -2a + b. We can start by substituting the given values of a and b in the expression.

Since a is between 3 and 5, the maximum value of -2a will be -2(3) = -6.

Similarly, since b is between 5 and 7, the minimum value of b will be 5, giving us a possible minimum value of -2a + b as -6 + 5 = -1. On the other hand, the minimum value of -2a will be -2(5) = -10, and the maximum value of b will be 7, giving us a possible maximum value of -2a + b as -10 + 7 = -3.

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Answer:

2000 ml or 2l

Step-by-step explanation:

The prove of expression is shown below.

Now, It is given that;

P = aˣ , q = [tex]a^{y}[/tex] and a⁴ = [tex](p^4^y q^4^x)^z[/tex]

And, we have to prove that xyz = 1/2.

Hence, We can simplify as;

Since, here a⁴ = [tex](p^4^y q^4^x)^z[/tex]

⇒ a⁴ = [tex][(a^x)^{4y} . (a^y)^4^x ]^z[/tex]

⇒a⁴ = [tex][a^{4xy} . a^{4xy} ]^z[/tex]

⇒a⁴ = [tex][a^{4xy + 4xy} ]^z[/tex]

⇒a⁴ = [tex](a^{8xy} )^{z}[/tex]

⇒a⁴ = [tex]a^{8xy} ^{z}[/tex]

⇒ 4 = 8xyz

⇒ xyz = 1/2

Thus, It can prove as shown.

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Question is,

If p = a^x, q = a^y and a^4 = (p^4y.q^4x)^z prove that xyz =1/2​

The expression xyz = 1/2 is proved.

The given exponential expressions are,

[tex]p = a^{x}[/tex]

[tex]q = a^{y}[/tex]

And [tex]a^{4} = (p^{4y} q^{4x}) ^{z}[/tex]

Now proceed the third expression,

[tex]a^{4} = (p^{4y} q^{4x}) ^{z}[/tex]

⇒[tex]a^{4} = ((a^{x} )^{4y} (a^{y} )^{4x}) ^{z}[/tex]

⇒[tex]a^{4} = (a^{4xy} a^{4xy}) ^{z}[/tex]

⇒[tex]a^{4} = (a^{8xy}) ^{z}[/tex]

⇒[tex]a^{4} = a^{8xyz}[/tex]

Now equate the exponents

⇒ 8xyz = 4

⇒   xyz = 1/2

Which was required.

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The complete question is :

If [tex]p = a^{x}[/tex], [tex]q = a^{y}[/tex] and  [tex]a^{4} = (p^{4y} q^{4x}) ^{z}[/tex] then prove that xyz =1/2​.

Answer:

Based on the illustration, it seems that the two materials used in the assembly are cast iron and aluminum (option E).

In order to achieve the shortest distance from starting vertex (A) to F on a network, utilize Dijkstra's algorithm following these steps:

Initiate every vertex with a tentative distance value: assign zero to the starting point and infinity to other vertices.

Establish the initiating vertex as the current vertex.

Analyze all neighboring vertices of the current vertex and determine their respective tentative path length via current vertex. Proceed to compare it with its already assigned value; upgrade such distance if shorter than before.

Subsequent to analyzing adjacent points of the present node, designate it as 'visited'. Futuristic reference will disregard this chosen and visited vertex altogether.

Examine unexplored vertices marked as having the most reduced tentative distances, declare them 'current' while formulating new calculations for other contenders until pertinent conclusion is reached.

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The 90% confidence interval for the number of chocolate chips per cookie for Big Chip cookies is given as follows:

[tex]5.8 < \mu < 7.8[/tex]

The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the following rule:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

In which the variables of the equation are presented as follows:

The critical value, using a t-distribution calculator, for a two-tailed 90% confidence interval, with 41 - 1 = 40 df, is t = 1.6839.

The parameters for the interval in this problem are given as follows:

[tex]\overline{x} = 6.8, s = 3.7[/tex]

The lower bound of the interval is given as follows:

6.8 - 1.6839 x 3.7/sqrt(41) = 5.8.

The upper bound of the interval is given as follows:

6.8 + 1.6839 x 3.7/sqrt(41) = 7.8.

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The offset section of machine depicts.

Hence option (C) is correct.

In the given figure

If machine is cut according the given manner

Then the three part be cut accordingly

Since the cut mark divides the machine segment into equal parts.

So after cutting of machine

We get offset section of each subparts.

Hence it shows offset section of machine.

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Answer:

[tex]g(x) = {x}^{2} + 5[/tex]

The graph shows g(x), which is a translation of [tex]f(x) = x^2[/tex]. The function rule for g(x) is [tex]x^2 + 5[/tex]. Hence, g(x) = [tex]\underline{x^2 + 5}[/tex]

Given, g(x) is a translation of [tex]f(x) = x^2[/tex]

Let the equation of the function g(x) be

[tex]g(x) = a(x - h)^2 + k[/tex] ----------(1)

This curve passes through the points (1, 6), (-1, 6) and (2, 9), then their coordinates satisfy the equation:

[tex]6 = a(1 - h)^2 + k[/tex]----------(2)

[tex]6 = a(-1 - h)^2 + k[/tex]----------(3)

[tex]9 = a(2 - h)^2 + k[/tex]----------(4)

Subtract (2) from the first:

[tex]6 - 6 = a(1 - h)^2 + k - a(-1 - h)^2 - k[/tex]

[tex]0 = a((1 - h)^2 - (-1 - h)^2)[/tex]

As a [tex]\neq[/tex] 0,

then [tex](1 - h)^2 - (-1 - h)^2 = 0[/tex]

[tex](1 - h)^2 = (-1 - h)^2[/tex]

[tex]1 - h = -1 - h[/tex],

or [tex]1 - h = 1 + h[/tex]

As, 1 = -1 is false

h = 0

Then, substituting h = 0 in (2) and (4),

[tex]6 = a(1 - 0)^2 + k[/tex]  ⇒ [tex]6 = a + k[/tex] ----------(5)

[tex]9 = a(2 - 0)^2 + k[/tex] ⇒ [tex]9 = 4a + k[/tex] ----------(6)

Solving (5) and (6) we get,

3a = 3

a = 1

Substituting a = 1 in (5),

6 = 1 + k ⇒ k = 5

Substituting a = 1, h = 0 and k = 5 in equation (1),

[tex]g(x) = x^2 + 5[/tex]

Therefore, the function rule for g(x) is [tex]x^2 + 5[/tex].

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The travelled distance of the traveller is equal to 195 kilometers.

According to the statement of the problem, a traveller already walked a third part of his trail and if he travels the half of his trail, then the half of his trail shall be covered. Mathematically, the travelled distance shall be described by following expression:

x = d / 3

x + 65 = d / 2

Where:

Now we proceed to determine the travelled distance:

d / 3 + 65 = d / 2

d / 2 - d / 3 = 65

3 · d - d = 390

2 · d = 390

d = 195

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You will spend 27 minutes in the doctor's office.

An exponential function has the definition presented as follows:

[tex]y = ab^x[/tex]

In which the parameters are given as follows:

The initial amount is of 14 mg, hence:

[tex]y = 14b^x[/tex]

After 16 minutes, the amount is of 4.5 mg, hence the parameter b is obtained as follows:

[tex]4.5 = 14b^{16}[/tex]

[tex]b^{16} = \frac{4.5}{14}[/tex]

[tex]b = \left(\frac{4.5}{14}\right)^{\frac{1}{16}}[/tex]

b = 0.931521.

Hence:

[tex]y = 14(0.931521)^x[/tex]

You will have 2 mg when:

[tex]2 = 14(0.931521)^x[/tex]

[tex](0.931521)^x = \frac{1}{7}[/tex]

x = log(1/7)/log(0.931521)

x = 27 minutes.

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The value of x make the two expressions equal is -2.2

From the question, we have the following parameters that can be used in our computation:

(x+3)(x+8)= 3/5(x+8)

Divide both sides of the equations by x + 8

So, we have the following representation

x + 3 = 3/5

Multiply through the equation by 5

So, we have

5x + 15 = 3

This gives

5x = -12

Divide both sides by 5

x = -12/5

Evaluate the quotient

x = -2.2

Hence the value of x is -2.2

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Answer:

3.14

Step-by-step explanation:

The value of pi to two decimal places is 3.14. It is a mathematical constant that represents the ratio of the circumference of a circle to its diameter. Pi is an irrational number, which means it cannot be expressed as a finite decimal or fraction. It is an important constant in many fields of mathematics and science, including geometry, trigonometry, and physics. The decimal representation of pi goes on infinitely without repeating, making it an interesting and challenging topic for mathematicians to explore.

Answer:

$17.8

Step-by-step explanation:

C= 15.00 + 0.07(40)

The probability of the spinner landing on blue is given as follows:

P(blue) = 0.45 = 45%.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The total number of trials for this problem is given as follows:

50 + 60 + 90 = 200 trials.

On 90 of these trials, the spinner landed on blue, hence the probability is given as follows:

p = 90/200 = 0.45 = 45%.

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The salesman traveled at an average speed of 55 miles per hour on his trip.

To find the average miles per hour, we need to find the total distance traveled and divide it by the total time taken.

Total distance traveled = 52 miles + 64 miles + 49 miles = 165 miles

Total time taken = 1 hour + 1 hour + 1 hour = 3 hours

Average speed = Total distance traveled / Total time taken

= 165 miles / 3 hours

= 55 miles per hour

Therefore, the salesman averaged 55 miles per hour on his trip.

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To solve this problem, we need to convert all the measurements to a consistent unit. Let's convert the height to inches since the height of the bounce is given in inches.

64 ft = 64 * 12 inches = 768 inches

Now, we can set up an equation to represent the height of each bounce. Let's use "b" to represent the number of bounces, and "h" to represent the height of each bounce in inches.

The height of each bounce is three-fourths (3/4) the height of the previous bounce. So, we can write the equation as:

h = (3/4) * h_previous

where h_previous is the height of the previous bounce.

We know that the initial height of the ball is 768 inches, and we want to find the number of bounces when the height of the bounce is less than 9 inches. We can set up an inequality to represent this situation:

h < 9

Substituting the expression for h from the equation above, we get:

(3/4) * h_previous < 9

Now, we can start with the initial height of 768 inches and keep applying the equation for each bounce until the height of the bounce is less than 9 inches.

1st bounce:

h = (3/4) * 768 = 576 inches

2nd bounce:

h = (3/4) * 576 = 432 inches

3rd bounce:

h = (3/4) * 432 = 324 inches

4th bounce:

h = (3/4) * 324 = 243 inches

5th bounce:

h = (3/4) * 243 = 182.25 inches

6th bounce:

h = (3/4) * 182.25 = 136.6875 inches

7th bounce:

h = (3/4) * 136.6875 = 102.515625 inches

8th bounce:

h = (3/4) * 102.515625 = 76.88671875 inches

9th bounce:

h = (3/4) * 76.88671875 = 57.6650390625 inches

10th bounce:

h = (3/4) * 57.6650390625 = 43.248779296875 inches

So, the ball will bounce up to a height less than 9 inches after 10 bounces.

The account will have $598.91 after 50 years.

Given that Kathy deposited $100 in an account for 40 years, the account has a 4.5% effective annual interest rate,

Therefore,

[tex]Amount = Deposit(1+r/4)^{4t[/tex]

[tex]= 100(1+0.1125)^{160[/tex]

= 598.91.

Hence, the account will have $598.91 after 50 years.

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30x + 40y ≤ 240 and 2x + y ≥ 8 are the required system of inequalities and the graph is given in attachment

Let x be the number of pages printed with layout a, and let y be the number of pages printed with layout y.

We want to maximize the number of pictures printed subject to the cost constraint.

The cost constraint can be expressed as:

30x + 40y ≤ 240

We also have a constraint on the number of pictures:

4x + 2y ≥ 16

This inequality can be simplified to:

2x + y ≥ 8

We can graph these inequalities on the xy-plane:

First, graph the line 30x + 40y = 240 by finding its intercepts:

x-intercept: 30x + 40y = 240 -> x = 8

y-intercept: 30x + 40y = 240 -> y = 6

So the line passes through the points (8,0) and (0,6).

Next, graph the line 2x + y = 8:

x-intercept: 2x + y = 8 -> x = 4

y-intercept: 2x + y = 8 -> y = 8

So the line passes through the points (4,0) and (0,8)

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The requried it takes 8.37 seconds for the object to hit the ground.

The polynomial 16T² - 1120 gives the height of the object in feet as a function of time T in seconds after it is dropped from a height of 1120 feet. When the object hits the ground, its height is zero. So we can set the polynomial equal to zero and solve for T:

16T² - 1120 = 0

T² - 70 = 0

T² = 70

T = ±√70

Since time cannot be negative, we can disregard the negative solution. Therefore, the object hits the ground after:

T = √70 ≈ 8.37 seconds

So it takes 8.37 seconds for the object to hit the ground.

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Answer:

(x*0) (y*3)

Step-by-step explanation:

times 3

The rate of change of the average height in feet of the trees on the farm with respect to the number of years since the trees were planted would be = 7ft/year. That is option C.

To calculate the rate of change of the average height of the trees in the farm the following is carried out.

The total heights of the tress that was recorded;

= 10+24+45+80+108

= 267 ft

The total number of years that was recorded;

= 1+3+6+12+15

= 37 years

Therefore the rate of change of the average height of the tress would be = 267/37 = 7 ft/yr.

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Joey could need to pay $3,825.00 per year in total Social security and Medicare tax if he operates his personal construction company as a self-employed individual. Therefore Option D is correct.

If Joey is self-employed and operates his personal construction organization, he would need to pay both the employee and organization portions of the Social safety and Medicare taxes. those taxes are together referred to as self-employment taxes.

The current self-employment tax charge for Social security is 12.4% on profits up to $142,800 (as of 2021) and the price for Medicare is two.9% and not using a earnings limit.

But, for the reason that Joey is each the worker and the employer, he might need to pay both portions, resulting in a total self-employment tax rate of 15.3%.

To calculate the full amount of Social security and Medicare tax that Joey would pay, we can multiply his profits of $25,000 via the self-employment tax fee of 15.3%:

$25,000 x 0.153 = $3,825.00

Therefore, Joey could need to pay $3,825.00 per year in total Social security and Medicare tax.

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The ratio of the number of baskets scored by team A to the number of baskets by team B is 2: 5. Then the correct option is B.

In a basketball game, team B scored 5 baskets for every 2 that team A scored.

The utilization of two or more additional numbers that compares is known as the ratio.

Assume that Team A scored two baskets while Team B netted five.

The problem statement states that for every two baskets Team A scored, Team B scored five. This may be expressed as the ratio shown below:

Ratio = 2x : 5x

Ratio = 2: 5

Thus, the correct option is B.

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We can see here that option C is the correct option that gives us the percentage bar graph that best represents the data.

A bar graph, also called a bar chart, is a form of graph that uses rectangular bars of equal width to depict data. Each bar's height or length reflects the value or frequency of the data it conveys. Discrete or categorical data are frequently compared and analyzed using bar graphs.

We see that from the data given, the total number of students =

44 + 55 + 55 + 66 = 220

Reading = 44/220 × 100% = 20%

Sports =  55/220 × 100% = 25%

Video Games =  55/220 × 100% = 25%

Music = 66/220 × 100% = 30%

Thus, option C is the correct answer.

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