in the diagram below, triangle PQR is similar to triangle STU. based on the diagram, select all the equations that are true.

Solution :

Given :

[tex]f(x) = \left\{\begin{matrix}\frac{1}{450}(x^2-x) & \text{if } 6 < x < 12 \\ 0 & \text{otherwise}\end{matrix}\right.[/tex]

1. Cumulative distribution function

[tex]$P(X \leq x) = \int_{- \infty}^x f(x) \ dx$[/tex]

              [tex]$=\int_{- \infty}^6 f(x) dx + \int_{6}^x f(x) dx $[/tex]

             [tex]$=0+\int_6^x \frac{1}{450}(x^2-x) \ dx$[/tex]

             [tex]$=\frac{1}{450} \int_6^x (x^2-x) \ dx$[/tex]

             [tex]$=\frac{1}{450}\left[\frac{x^3}{3}-\frac{x^2}{2}\right]_6^x$[/tex]

             [tex]$=\frac{1}{450}\left[ \left( \frac{x^3}{3} - \frac{x^2}{2}\left) - \left( \frac{6^3}{3} - \frac{6^2}{2} \right) \right] $[/tex]

            [tex]$=\frac{1}{450}\left[\frac{x^3}{3} - \frac{x^2}{2} - 54 \right]$[/tex]

2.  Mean [tex]$E(x) = \int_{- \infty}^{\infty} \ x \ f(x) \ dx$[/tex]

                       [tex]$=\int_{6}^{12}x . \left( \frac{1}{450} \ (x^2-x)\right)\ dx$[/tex]

                     [tex]$=\frac{1}{450} \int_6^{12} \ (x^3 - x^2) \ dx$[/tex]

                     [tex]$=\frac{1}{450} \left[\frac{x^4}{4} - \frac{x^3}{3} \right]_6^{12} \ dx$[/tex]

                     [tex]$=\frac{1}{450} \left[ \left(\frac{(12)^4}{4} - \frac{(12)^3}{3} \right) - \left(\frac{(6)^4}{4} - \frac{(6)^3}{3} \right) $[/tex]

                     [tex]$=\frac{1}{450} [4608 - 252]$[/tex]

                    = 17.2857

Answer:

80 telephones should be sampled

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

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

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error is of:

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

89% confidence level

So [tex]\alpha = 0.11[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.11}{2} = 0.945[/tex], so [tex]Z = 1.6[/tex].

How many telephones should be sampled and checked in order to estimate the proportion defective to within 9 percentage points with 89% confidence?

n telephones should be sampled, an n is found when M = 0.09. We have no estimate for the proportion, thus we use [tex]\pi = 0.5[/tex]

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

[tex]0.09 = 1.6\sqrt{\frac{0.5*0.5}{n}}[/tex]

[tex]0.09\sqrt{n} = 1.6*0.5[/tex]

[tex]\sqrt{n} = \frac{1.6*0.5}{0.09}[/tex]

[tex](\sqrt{n})^2 = (\frac{1.6*0.5}{0.09})^2[/tex]

[tex]n = 79.01[/tex]

Rounding up(as 79 gives a margin of error slightly above the desired value).

80 telephones should be sampled

9514 1404 393

Answer:

  d = kw/p

Step-by-step explanation:

When d varies directly with w, the equation is ...

  d = kw

When d varies inversely with p, the equation is ...

  d = k/p

When d does both, the equation is ...

  d = kw/p

Answer:

D = all reals (or -7 to 7)

Step-by-step explanation:

If the line continues on for infinity, then the domain is all reals, or negative infinity to positive infinity. If the line ends on the graph that we can see, though, the domain would be [-7 , 7]

Answer:

x = 3

Step-by-step explanation:

A midsegment in a trapezoid is formed when one connects the midpoints of the two legs (non-parallel sides) in a trapezoid. The midsegment theorem states that the length of the midsegment is equal to the average of the two bases (that is the parallel sides).

One can apply the midsegment theorem here by stating the following;

[tex]\frac{(YZ)+(TM)}{2}=PW[/tex]

Substitute,

[tex]\frac{23+11x+2}{2}=29[/tex]

Simplify,

[tex]\frac{25+11x}{2}=29[/tex]

Inverse operations,

[tex]\frac{25+11x}{2}=29[/tex]

[tex]25+11x=58\\\\11x = 33\\\\x = 3[/tex]

Answer:

(73.845 ; 76.155) ;

(41.633 ; 48.367) ;

1.273 ;

C. With 99% confidence, the mean width of all widgets is between 11.8 and 20.4. ;

1.717

Step-by-step explanation:

1.)

Given :

Mean, xbar = 75

Sample size, n = 24

Sample standard deviation, s = 3.3

α = 90%

Confidence interval = mean ± margin of error

Margin of Error = Tcritical * s/√n

Tcritical at 90% ; df = 24 - 1 = 23

Tcritical = 1.714

Margin of Error = 1.714 * 3.3/√24 = 1.155

Confidence interval = 75 ± 1.155

Confidence interval = (73.845 ; 76.155)

2.)

Given :

Mean, xbar = 45

Sample size, n = 37

Sample standard deviation, s = 10.1

α = 95%

Confidence interval = mean ± margin of error

Margin of Error = Tcritical * s/√n

Tcritical at 95% ; df = 37 - 1 = 36

Tcritical = 2.028

Margin of Error = 2.028 * 10.1/√37 = 3.367

Confidence interval = 45 ± 3.367

Confidence interval = (41.633 ; 48.367)

3.)

Given :

Mean, xbar = 37

Sample size, n = 30

Sample standard deviation, s = 4.1

α = 90%

Margin of Error = Tcritical * s/√n

Tcritical at 90% ; df = 30 - 1 = 29

Tcritical = 1.700

Margin of Error = 1.700 * 4.1/√30 = 1.273

5.)

Sample size, n = 23

Confidence level, = 90%

df = n - 1 ; 23 - 1 = 22

Tcritical(0.05, 22) = 1.717

Answer:

5%

Step-by-step explanation:

Hospital A (with 50 births a day), because the more births you see, the closer the proportions will be to 0.5.

Hospital B (with 10 births a day), because with fewer births there will be less variability.

The two hospitals are equally likely to record such an event, because the probability of a boy does not depend on the number of births

Two hospitals have an equal chance of recording such an event.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Given

Hospital A (with 50 births per day), as the proportions will be closer to 0.5 the more births you see.

Hospital B (with 10 births per day), thus there will be less unpredictability with fewer births.

Due to the fact that the likelihood of a boy does not rely on the number of births, the two hospitals have an equal chance of recording such an event.

To learn more about probability refer to:

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Answer:

Most Likely A, 5.5 Miles

Step-by-step explanation:

However the question doesn't make sense as the logical answer is simply 5 miles, but the safest choice is 5.5

Answer:

16 cm

Step-by-step explanation:

4 + 4 + 3 + 5 = 16

The = sign means that B (which is 4 cm) is equal to D (which had no number)

And because it says that B = D (with the squiggly line (or a tilde)) And the L's (which means that the letters represent an angle) All you have to do is add the numbers together, and you get 16.

Sorry if I explained it badly, you at least got the answer.

(And also, if I'm wrong, please tell me.)

Answer:

P = 32 cm

Step-by-step explanation:

Im just putting the right answer up so you don't accidentally put in the wrong one.

Answer:

C. 37.8 units

Step-by-step explanation:

ED = 17/ cos(38°) = 17 / 0.7880 = 21.6 units

DF = 17× tan (38°) = 17× 0.7813 = 13.3 units

CD = 10/13.3 × 21.6 = 16.2 units

so, the length of CE = 21.6+16.2 = 37.8 units

The equation of the hyperbola is,

(x/12)² - 4y²/(527) = 1

The standard equation of the hyperbola is

(x/a)² - (y/b)² = 1

Here (a, 0) and (-a, 0) are vertices and asymptotes y = ± √(b/a)x

Foci are (c, 0) & (-c, 0)

Then a² + b² = c²

Here we have to give that.,

2a = 24

a = 12

And 2c = 7

c = 7/2

Therefore a = 12 and c = 3.5

Substituting a and c in Pythagorean identity;

b² = 527/4

Then, the equation of the hyperbola is

(x/12)² - 4y²/(527) = 1

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We have b = 0, which implies that the foci coincide with the vertices, making the hyperbola a degenerate case. In this scenario, the equation of the border would be a vertical line passing through the vertices/foci, given by the equation x = ±a.

To find the equation of the hyperbolic border created by the shadow on the wall, we can start by understanding the properties of a hyperbola. A hyperbola is defined as the set of all points such that the difference of the distances from any point on the hyperbola to two fixed points, called the foci, is constant.

Let's label the vertices of the hyperbola as A and B, and the foci as F1 and F2. The distance between the vertices is given as 2a inches, and the foci are located at a distance c inches from the vertices.

Using the given information, we can find the value of a and c. Since the center of the hyperbola is at the origin, the coordinates of the vertices are (±a, 0), and the coordinates of the foci are (±c, 0).

The distance between the foci is given by the equation:

c = √(a^2 + b^2)

We know that the distance between the foci is given as 2c inches, so:

2c = 2√(a^2 + b^2)

Since c is given as a distance from the vertices, we can substitute c = a - b to simplify the equation:

2(a - b) = 2√(a^2 + b^2)

Squaring both sides to eliminate the square root:

4(a - b)^2 = 4(a^2 + b^2)

Expanding the equation:

4(a^2 - 2ab + b^2) = 4a^2 + 4b^2

Simplifying the equation:

4a^2 - 8ab + 4b^2 = 4a^2 + 4b^2

Canceling out the common terms:

-8ab = 0

Dividing by -8:

ab = 0

This implies that either a = 0 or b = 0. However, since a represents the distance between the vertices and b represents the distance between the foci and vertices, we can rule out a = 0 as it would result in a degenerate hyperbola.

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Answer:

12/13 is the answer

Step-by-step explanation:

Answer:

£1054.729

Step-by-step explanation:

To find compound interest you need to use the equation 1000(1.027)^x.

To find the interest rate (1.027):

100 + 2.7 = 102.7

102.7 / 100 = 1.027

The value of x is the amount of months if no payment is made in this situation, so 2 would be the x value for this problem.

Hope this helps!  

Answer:

The diameter that separates the top 3% is of 5.85 millimeters, and the one which separates the bottom 3% is of 5.55 millimeters.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

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

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean of 5.7 millimeters and a standard deviation of 0.08 millimeters.

This means that [tex]\mu = 5.7, \sigma = 0.08[/tex]

Top 3%

The 100 - 3 = 97th percentile, which is X when Z has a p-value of 0.97, so X when Z = 1.88.

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

[tex]1.88 = \frac{X - 5.7}{0.08}[/tex]

[tex]X - 5.7 = 1.88*0.08[/tex]

[tex]X = 5.85[/tex]

Bottom 3%

The 3rd percentile, which is X when Z has a p-value of 0.03, so X when Z = -1.88.

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

[tex]-1.88 = \frac{X - 5.7}{0.08}[/tex]

[tex]X - 5.7 = -1.88*0.08[/tex]

[tex]X = 5.55[/tex]

The diameter that separates the top 3% is of 5.85 millimeters, and the one which separates the bottom 3% is of 5.55 millimeters.

Answer:

The ocean surface is at 0 ft elevation. A diver is underwater at a depth of 138 ft. In this area, the ocean floor has a depth of 247 ft.

Step-by-step explanation:

Step-by-step explanation:

this is the answerI hope it helps

Answer:

The answer is 65

Step-by-step explanation:

Evaluate:

8x + 9

When x = 7

Use PEMDAS order of operations:

8x + 9

= 8(7) + 9

= 56 + 9

= 65

Hope this helps

Answer:

the answer here is d

the answer is d

Answer:

28

Step-by-step explanation:

Total number of crayons = 32

Number of crayons lost = 4

Therefore, number of crayons she is left with is : 32 - 4 = 28

Working :  

    [tex]32\\04 - \\\overline{28}[/tex]

Answer:

150 m at 10 m/s

350 m at 50 m/s

Step-by-step explanation:

x + y = 500

x/10 + y/50 = 22

~~~~~~~~~~~~~~~~~

x + y = 500

5x  + y  = 1100

~~~~~~~~~~~~~~~~

x + y = 500

-5x  - y  = -1100

-4x = -600

x = 150

y = 350

Answer:

D

Step-by-step explanation:

solution is the points where the two graphs intersect.

they intersect at (-3,-3) and (0,6)

Answer:

Option C: QT < TR

Step-by-step explanation:

From the triangle, we can see that UX bisects RS into two equal parts and so it is a perpendicular bisector.

TZ Is a mid segment and it means that T bisects QR into 2 equal parts as well as QS into 2 equal parts.

Thus;

QT = QR

And QZ = SZ

So Option C is not correct because QT = QR

Answer:

the answer should be e^3

Step-by-step explanation:

i hope it helps you

Answer:

Pizza = 12.35

Chips = 2.75

Step-by-step explanation:

Let :

Pizza = x

chips = y

3x + 4y = 48.05 - - - (1)

5x + 2y = 67.25 - - - (2)

Multiply (1) by 5 and (2) by 3

15x + 20y = 240.25

15x + 6y = 201.75

Subtract :

20y - 6y = 240.25 - 201.75

14y = 38.50

y = 38.50/ 14

y = 2.75

Put y = 2.75 in (1)

3x + 4(2.75) = 48.05

3x + 11 = 48.05

3x = 48.05 - 11

3x = 37.05

x = 37.05 / 3

x = 12.35

Pizza = 12.35

Chips = 2.75

Answer:

(3) $20.1 billion

Step-by-step explanation:

hope it help

Answer:

(5) $60.3 billion​

Step-by-step explanation:

Answer:

B. 8.114

Step-by-step explanation:

The intercept parameter is the zero-grade component of the multilinear equation, that is, the component independent from [tex]x_{1}[/tex] and [tex]x_{2}[/tex]. Hence, the intercept parameter of the multilinear regression is 8.114. (Correct answer: B)

Answer:

x = -4   or   x = 5

Step-by-step explanation:

To solve the absolute value equation

|X| = k

where X is an expression in x, and k is a non-negative number,

solve the compound equation

X = k or X = -k

Here we have |2 - 4x| = 18

In this problem, the expression, X, is 2 - 4x, and the number, k, is 18.

We set the expression equal to the number, 2 - 4x = 18, and we set the expression equal to the negative of the number, 2 - 4x = -18. Then we solve both equations.

2 - 4x = 18  or  2 - 4x = -18

-4x = 16   or   -4x = -20

x = -4   or   x = 5

Answer:

x = -5 . x= 4

Step-by-step explanation:

because |4| = 4 and |-4| = 4

you can see that TWO inputs can get an output of (lets say) 4

The absolute value function can be seen as a function that ignores negative signs

so to get an OUTPUT of "18" using the absolute value function

there are really two ways of getting there

"2-4x = 18"  AND "2-4x = -18"

if you solve both of those you will find that -5 and 4 will

produce the 18 and -18

Answer:

Andres

why?

Because he is median salary for cpa

Step-by-step explanation:

here is the answer to your question