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What is the area of the trapezoid?

33 in2
52.5 in2
82.5 in2
91 in2

Using the Fundamental Counting Theorem, it is found that:

a) 256 codes are possible.

b) The probability is [tex]\frac{1}{256}[/tex].

It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

There are 4 keys, each with 4 options, hence the parameters are:

[tex]n_1 = n_2 = n_3 = n_4 = 4[/tex].

Then the number of codes is:

[tex]N = 4^4 = 256[/tex]

And the probability is:

[tex]p = \frac{1}{256}[/tex].

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Refractory period brief time-out of the heart's electrical impulse that allows for sufficient time for ventricular filling between beats.

End-diastolic pressure is at its resting level (end-diastolic pressure) and ventricular volumes are at their maximum value when the heart muscle is relaxed (end-diastolic volume).

What is the state of the heart during systole?

What are the 4 phases of cardiac cycle?

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The factorise form of the two expression are as follows:

b. (x - 3)(2 / 3 x - 6) = 0

Therefore, let's open the brackets

2 / 3 x² - 6x -2x + 18 = 0

2 / 3 x²  - 8x + 18 = 0

multiply through by 3

2x² - 24x + 54 = 0

Hence,

 2 (x - 3)  (x - 9)

c.

(-3x - 15)(x + 7)  = 0

Therefore,

-3x² - 21x - 15x - 105 = 0

-3x² - 36x - 105 = 0

-3(x + 5)(x + 7)

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Answer:

98

Step-by-step explanation:

96+100=196

196÷2=98

Answer:

97.

Step-by-step explanation:

86 96 100 98

Place them in order:

86 96 98 100

The median is the middle value of an ascending sequence of numbers.

As there is an even number of values the median is the mean of the 2 middle ones:

So here it is (96 + 98) / 2

= 97.

The probability that a kid who goes to the doctor has a sore throat given that he has a fever is 30%

The given parameters are:

P(Fever) = 70%

P(Fever and sore throat) = 21%

The probability that a kid who goes to the doctor has a sore throat given that he has a fever is calculated as:

P = P(Fever and sore throat)/P(Fever)

So, we have:

P = 21%/70%

Evaluate

P = 30%

Hence, the probability is 30%

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Answer:

  the equation is no longer quadratic

Step-by-step explanation:

A quadratic equation is a polynomial equation in which the highest-degree term has degree 2.

The value a=0 makes the squared term disappear. If 'a' is zero, the equation becomes a linear equation, not a quadratic equation:

  bx +c = 0

Answer:

$13.20

Step-by-step explanation:

A dozen consists of 12 items. If you have 3 you must multiply the current amount by 4 to get 12. Therefore you must also multiply the price by 4.

3.30*4=13.20

Explanation:

The proof can be had by making use of the AAS congruence postulate (twice) and CPCTC.

We start by showing ΔPQY≅ΔPRX, then by showing ΔXQN≅ΔYRN. The proof is then a result of CPCTC.

1. PQ≅PR, ∠Q≅∠R . . . . given

2. ∠P≅∠P . . . . reflexive property of congruence

3. ΔPQY≅ΔPRX . . . . AAS congruence postulate

4. PX≅PY . . . . CPCTC

5. PX+XQ=PQ, PY+YR=PR . . . . segment sum theorem

6. PX+XQ = PY +YR . . . . substitution property

7. PX +XQ = PX +YR . . . . substitution property

8. XQ = YR . . . . subtraction property of equality

9. ∠XNQ≅∠YNR . . . . vertical angles are congruent

10. ΔXNQ≅ΔYNR . . . . AAS congruence postulate

11. XN ≅ YN . . . . CPCTC

__

Additional comment

You probably did steps 1-3 in part (a) of the problem.

Using the z-distribution, it is found that the 95% confidence interval for the proportion of college students who work to pay for tuition and living expenses is: (0.4239, 0.5161).

If we had increased the confidence level, the margin of error also would have increased.

A confidence interval of proportions is given by:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which:

In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96. Increasing the confidence level, z also increases, hence the margin of error also would have increased.

The sample size and the estimate are given as follows:

[tex]n = 450, \pi = 0.47[/tex].

The lower and the upper bound of the interval are given, respectively, by:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.47 - 1.96\sqrt{\frac{0.47(0.53)}{450}} = 0.4239[/tex]

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.47 + 1.96\sqrt{\frac{0.47(0.53)}{450}} = 0.5161[/tex]

The 95% confidence interval for the proportion of college students who work to pay for tuition and living expenses is: (0.4239, 0.5161).

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Average speed of Alishia is 19 kilometers per hour

Average speed is calculated by dividing the total distance that something has traveled by the total amount of time it took it to travel that distance. Speed is how fast something is going at a particular moment. Average speed measures the average rate of speed over the extent of a trip

Given :

Distance = 45.3 km

Time taken = 143 minutes = 143/60 =2.384 hours

∴ Average speed = 45.3/2.384 = 19 kilometers per hour

Thus the average speed of Alishia is 19 kilometers per hour.

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Answer:

X multiplied by 2 is 8

X divided by 2 is 4

Step-by-step explanation:

This is the quickest thing i can give you

The value of the constant of variation include 8, 3.2, and 1.25

From the information given, when x = -0.5, y = -4.0. The constant will be:

y = kx

-4 = -0.5k

k = -4.0/-0.5

k. = 8

When x = 2.5, y = 8

y = kx

8 = 2.5k

k = 8/2.5

k = 3.2

When x = 4, y = 5

y = kx

5 = 4k

k = 5/4

k = 1.25

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The solution to the equation is 2

Given the equation

4 + 4(x-2) = 2(x+1) - x

First, we expand the bracket

4 + 4x - 8 = 2x + 2 - x

collect like terms

4x - 2x + x = 2 - 4 + 8

Add like terms

3x = 6

Make 'x' the subject

x = 6/3

x = 2

Thus, the solution to the equation is 2

The complete question is

What is the solution to the equation of 4 + 4(x-2) = 2(x+1) - x? show your work

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Answer:

probability of choosing two women over people in a community=⅔

Triangles ABC and DEF are similar. The scale factor for the pair is: 1/6.

The ratios of the corresponding sides of similar triangles are equal, because they are proportional.

If triangles ABC and DEF are similar triangles, then:

AB/DE = BC/EF = AC/DF

Plug in the given values

2/12 = 5/30 = 6/36 = 1/6

This means that the triangles are certianly similar. The scale factor for the pair is: 1/6.

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Considering that the value of 126.07 is valid for the population, it is a parameter.

In this problem, the mean blood pressure is calculated for all employees, which means that it is valid for the population, hence it is a parameter.

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The percentage of this plane that's enclosed by the pentagons is closest to: D. 56.

Since the side of the small square is a, then the area of the tile is

given by:

Area of tiles = 9a²

Note: With an area of 9a², 4a² is covered by squares while 5a² by pentagons.

This ultimately implies that, 5/9 of the tiles are covered by pentagons and this can be expressed as a percentage as follows:

Percent = 5/9 × 100

Percent = 0.555 × 100

Percent = 55.5 ≈ 56%.

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Complete Question:

The plane is tiled by congruent squares of side length a and congruent pentagons of side lengths a and a²/a, as arranged in the diagram below. The percent of the plane that is enclosed by the pentagons is closest to (A) 50 (B) 52 (C) 54 (D) 56 (E) 58

Answer:

D.

Step-by-step explanation:

Standard deviation tells us the dispersion of data/scores around the mean.

We can say that the standard deviation tells us the dispersion of the scores, making option D the correct choice.

A standard deviation (or σ) is a measure of how widely distributed the data is about the mean (μ). A low standard deviation suggests that data is grouped around the mean, whereas a large standard deviation shows that data is more spread out. A standard deviation around 0 suggests that data points are close to the mean, whereas a high or low standard deviation indicates that data points are above or below the mean, respectively.

We use the following formula to compute the standard deviation:

[tex]\sigma = \sqrt\frac{{\sum_{i=1}^{N}\left | x_i - \mu \right | }^2}{N}[/tex]

In this formula, σ is the standard deviation, [tex]x_i[/tex] is the data point in the set we are solving for, μ is the mean, and N is the total number of data points.

In the question, we are asked to tell what standard deviations tell us from the given options.

From the above discussion, we can say that the standard deviation tells us the dispersion of the scores, making option D the correct choice.

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Answer:

B

Step-by-step explanation:

Finding the area of the trapezoid using the lengths in the diagram, we get (c)(2d+a+b)/2.

This is equal to c(d+b), so:

(1/2)(c)(2d+a+b)=c(d+b)

(1/2)(2d+a+b)=d+b

d+0.5a+0.5b=d+b

0.5a+0.5b=b

0.5a=0.5b

a=b

Answer: R: {f(x) ∈ ℝ | f(x) ≥ 4}

Step-by-step explanation:

[tex]|x-3| \geq 0[/tex] for all real x, so the range is [tex]f(x) \geq 4[/tex].

The 95 percent confidence interval for the mean is (266.76,426.24).

A confidence interval is how much uncertainty there is with any particular statistic. Confidence intervals are often used with a margin of error. It tells you how confident you can be that the results from a poll or survey reflect what you would expect to find if it were possible to survey the entire population. Confidence intervals are intrinsically connected to confidence levels.

The formula of Confidence Interval =  Mean ±   [tex]t\frac{Standard Deviation}{\sqrt{number of observations} }[/tex]

where t is a constant

Given:

Mean = 346.5

Standard Deviation = 170.378

t-critical value for 95% Confidence interval with degrees of freedom(df)=n-1= 19 is 2.093

∴ Substituting values in formula we get

E = [tex]2.093 X170.378/\sqrt{20}[/tex] = 2.0931.96 x 38.0976=79.74

95% Confidence interval : (346.5-79.74,346.5+79.74)

95% Confidence interval : (266.76,426.24)

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[tex] \frac{(6x - 4)(3 - 2x)}{(4x - 6)} = \frac{2(3x - 2)(3 - 2x)}{2(2x - 3)} [/tex]

[tex] \frac{2(3x - 2)(3 - 2x)}{2(2x - 3)} = \frac{(3x - 2)(3 - 2x)}{(2x - 3)} [/tex]

[tex] \frac{(3x - 2)(3 - 2x)}{(2x - 3)} = \frac{ - (3x - 2)(2x - 3)}{(2x - 3)} [/tex]

[tex] \frac{ - (3x - 2)(2x - 3)}{(2x - 3)} = - (3x - 2)[/tex]

[tex] - (3x - 2) = 2 - 3x[/tex]

Using the normal distribution, there is a 0.6826 = 68.26% probability that the sample mean will be within 2 points of the population mean.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

For this problem, the parameters are given as follows:

[tex]\mu = 40, \sigma = 8, n = 16, s = \frac{8}{\sqrt{16}} = 2[/tex]

The probability that the sample mean will be within 2 points of the population mean is the p-value of Z when X = 40 + 2 = 42 subtracted by the p-value of Z when X = 40 - 2 = 38, hence:

X = 42:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

Z = (42 - 40)/2

Z = 1

Z = 1 has a p-value of 0.8413.

X = 38:

[tex]Z = \frac{X - \mu}{s}[/tex]

Z = (38 - 40)/2

Z = -1

Z = -1 has a p-value of 0.1587.

0.8413 - 0.1587 = 0.6826 = 68.26% probability that the sample mean will be within 2 points of the population mean.

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The relationship which best defines a function, for the houses on Katrina's street exists appraised value, property tax.

Table exists a form to describe the data of the two or more variables.

To read the data from the table, examine for the value of one variable, and obtain the resultant value of other variables from the related block.

The table below details some of the characteristics of the houses on Katrina’s street. Let's estimate the most suitable choice whose relationship defines a function.

The relationship which nicely illustrates the function, of the houses on Katrina's street exists between the appraised value and property tax.

Therefore, the correct answer is option d) (appraised value, property tax).

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Answer: D

Step-by-step explanation: Appraised Value , Property Tax

Perimeter of rectangle is 8x and Area is 3x^2 + 2x -1..

Lets try to solve out the problem,

Length = 3x-1

Width = x+1

Perimeter = 2(l+b)

Area = l*b

Perimeter= 2 (3x-1 + x+1)

P= 8x

Area = (3x-1) (x+1)

=> 3x(x+1) -1 (x+1)

=> 3x^2 + 3x -x -1

=> 3x^2 + 2x -1.

Hence Perimeter of rectangle is 8x and Area is 3x^2 + 2x -1..

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The  statements that are correct  about right triangle QRS are:

A right triangle posses  a right angle which is in opposite direction to the  hypotenuse.

Considering the right angle triangle, it can be deduced that Side opposite ∠Q is RS not RQ,  and  Adjacent side to ∠Q is QS.

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Answer:

see explanation

Step-by-step explanation:

(a)

(the side required )² = sum of squares of other 2 sides - ( 2 × product of other 2 sides and cos(angle opposite side required ) )

x² = 12² + 15² - (2 × 12 × 15 × cos71°)

(b)

x² = 144 + 225 - 360cos71°

   = 369 - 360cos71° ( take square root of both sides )

x = [tex]\sqrt{369-360cos71}[/tex]

  ≈ 16 cm ( to the nearest integer )

Answer:

The total surface area of the the cylinder is 640.56cm², surface are is always give in cm² not in cm³ b/c cm³ indicates the volume of the cylinder not the surface area.

Step-by-step explanation:

Hello!

. SA=2πr(r+h) ,or 2πr²+h(2πr)

Answer:

204π cm^2

which is 640.88 cm^2 to the nearest hundredth.

Step-by-step explanation:

Surface area = 2 * area of the base + area of the curved side.

= 2*π *r^2  + 2*π*r*h

= 2π(6)^2 + 2π(6)(11)

= 72π + 132π

= 204π cm^2.

Joel spent 72.5% of his time exercising after playing soccer on Tuesda

The given parameters are

Minutes spent on Tuesday = 27 more minutes than Monday

Total minutes spend = 60

This means that

Tuesday = Monday + 27

Monday + Tuesday = 60

Make Monday the subject in Tuesday = Monday + 27

Monday = Tuesday - 27

Substitute Monday = Tuesday - 27 in Monday + Tuesday = 60

Tuesday - 27 + Tuesday = 60

Evaluate

2 * Tuesday = 87

Divide by 2

Tuesday = 43.5

The percentage of time spent exercising on Tuesday is then calculated as

Percentage = 43.5/60 * 100%

Evaluate the expression

Percentage = 72.5%

Hence, Joel spent 72.5% of his time exercising after playing soccer on Tuesday

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