Use intercepts to graph the line described by the equation −2x − 5y = −20.

Answer:

[tex]\sqrt{\frac{15}{2} }[/tex] or 2.738

Step-by-step explanation:

Let’s just look at the triangle on the top with the [tex]\sqrt{10}[/tex] on the top and x on the bottom. (Basically the top half to the equilateral triangle)

There is a small square in the bottom right corner, which indicates that this triangle is a right triangle. This means that we can use the Pythagorean Theorem: [tex]a^{2} +b^{2} =c^{2}[/tex]

We know that \sqrt{10} is our hypotenuse, and therefore our c in our equation. Let’s say that x=a in our equation. Therefore we are left to find b. However, b is half the length of the side of the original equilateral triangle. An equilateral triangle means that all three sides are the same length. Therefore our side would also be \sqrt{10} units long. However we know that b is half of that value, so b=[tex]\frac{1}{2}(\sqrt{10})[/tex] or [tex]\frac{\sqrt{10} }{2}[/tex]

Plugging these values into the equation:

x^2+ (\frac{\sqrt{10} }{2})^{2}=\sqrt{10} ^{2}

[tex]x^{2}=\sqrt{10} ^{2}-\frac{\sqrt{10} }{2} ^{2}[/tex]

[tex]x^{2} =10-\frac{10}{4}[/tex]

[tex]x^{2} =\frac{15}{2}[/tex]

[tex]x=\sqrt{\frac{15}{2} }[/tex]

This approximately equals 2.738

Answer:

[tex]x=\sqrt{\frac{15}{2} }[/tex]. Another form of this answer is [tex]x=\frac{\sqrt{15} }{\sqrt{2} }[/tex](it's the same thing)

Step-by-step explanation:

Because the triangle is equilateral, all other sides of the triangle are also [tex]\sqrt{10}[/tex]. Also, x is the altitude of this triangle as it forms a right angle with the base and is therefore perpendicular. We know that this triangle is equilateral and in any triangle that has at least two sides that are equal(in other words isosceles), the altitude is also the median and angle bisector. A median would cut the side it reaches into half. So, x would cut the base into two equal parts. Since the base is [tex]\sqrt{10}[/tex], divide it by two and both halves are [tex]\frac{\sqrt{10}}{2}[/tex]. What we are left with is two right triangles, both with legs [tex]\frac{\sqrt{10} }{2}[/tex] and x. Using the Pythagorean Theorem, we know that [tex]a^{2}+b^{2}=c^{2}[/tex], with [tex]a[/tex] and [tex]b[/tex] being the legs and [tex]c[/tex] being the hypotenuse. So, we plug in the values and get [tex]\frac{\sqrt{10} }{2} ^{2}[/tex][tex]+x^{2}=\sqrt{10}^{2}[/tex]. Squaring, we get [tex]\frac{10}{4}+x^{2}=10[/tex]. This becomes [tex]x^{2}=10-\frac{10}{4}[/tex] which equals [tex]x^{2}=\frac{40}{4}-\frac{10}{4}[/tex]. Finally, [tex]x^{2}=\frac{30}{4}[/tex]. This is [tex]x^{2}=\frac{15}{2}[/tex]. Square rooting this we get [tex]x=\sqrt{\frac{15}{2} }[/tex]. Another form of this answer is [tex]x=\frac{\sqrt{15} }{\sqrt{2} }[/tex]

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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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

Answer:

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

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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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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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 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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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:

70 degrees.

Step-by-step explanation:

As AB is a diameter M < C = 90 degrees.

Therefore m < B = 90 - 20 = 70.

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 )

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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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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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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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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The time taken for Jenny to run the same distance at 10% faster is 13.05 seconds

Time taken by Jenny = 14.5 - (10% × 14.5)

= 14.5 - (0.1 × 14.5)

= 14.5 - (1.45)

= 13.05 seconds

Therefore, the time taken for Jenny to run the same distance is 13.05 seconds

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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:

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 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 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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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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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

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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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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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

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

[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]

The inverse of the function f(x)= 2x/7 + 4 is y = 7x/2 - 14.

Given the function; f(x)= 2x/7 + 4

First. we write the function as an equation then interchange the variables.

y = 2x/7 + 4

x = 2y/7 + 4

We solve for y.

2y/7 = x - 4

2y = 7x - 28

y = 7x/2 - 28/2

y = 7x/2 - 14

Therefore, the inverse of the function f(x)= 2x/7 + 4 is y = 7x/2 - 14.

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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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