Given: PQ is the


perpendicular bisector of XY


Prove: PX=PY

a. The probability that the system will operate as shown is approximately 0.6141.

b. Probability ≈ 0.6141The probability remains the same as in the previous case, which is approximately 0.6141.

c. The probability that the system will operate with each component having a backup with a probability of 0.85 and a switch that is 90% reliable is approximately 0.6485.

a. To find the probability that the system will operate as shown, we multiply the probabilities of each component. Since the system is shown to have three components with a probability of 0.85 each, we can calculate:

Probability = 0.85 × 0.85 × 0.85

Probability ≈ 0.6141

The probability that the system will operate as shown is approximately 0.6141.

b. In this case, each system component has a backup with a probability of 0.85 and a switch that is 100% reliable. Since the backup has a probability of 0.85, and the switch is 100% reliable (probability = 1), we can calculate the probability as:

Probability = 0.85 × 0.85 × 0.85

Probability ≈ 0.6141The probability remains the same as in the previous case, which is approximately 0.6141.

c. In this scenario, each system component has a backup with a probability of 0.85, but the switch is 90% reliable (probability = 0.90). We can calculate the probability as:

Probability = 0.85 × 0.90 × 0.85

Probability ≈ 0.6485

The probability that the system will operate with each component having a backup with a probability of 0.85 and a switch that is 90% reliable is approximately 0.6485.

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Answer:

336

Step-by-step explanation:

12+12=24 the base

18+10=28 the height

1/2 * 28 * 24 =336

Answer:

Area is 336.

Step-by-step explanation:

A=1/2bh

A=1/2 * 12+12 * 10+18

A=1/2 *672

A=336

Answer:

Step-by-step explanation:

The surface area of a square pyramid = 1/2 * slant height * base perimeter + area of base

 The slant height is 5 cm

The base perimeter is 4 * 5 cm = 20 cm

The area of the base is 5 cm * 5 cm = 25 cm**2

Plugging into the formula the area =

1/2 * 5 cm * 20 cm + 25 cm**2 =

5 cm * 10 cm + 25 cm**2 =

50 cm**2 + 25 cm**2 = 75 cm**2

Given the graph of the line and it is required to find the equation of the line.

As shown the line pass through the points ( 0 , 1080 ) and ( 6 , 810 )

Let the months = x and $ Owed = y

The general equation of the line in slope - intercept form is ;

Where m is the slope and b is y-intercept

The slope = Rise/Run

Rise = 810 - 1080 = -270

Run = 6 - 0 = 6

so, the slope :

And y - intercept is the value of y when x = 0

so, when x = 0 , y = 1080

So,

Therefore the equation of the line will be:

i) The Newton-Raphson iterative formula for finding the roots of an equation f(y) = 0 is given by:

yn+1 = yn - f(yn)/f'(yn)

For the function f(y) = y^3 - 2y - 5, we have:

f'(y) = 3y^2 - 2

Substituting these expressions for f(y) and f'(y) into the Newton-Raphson formula, we get:

yn+1 = yn - (yn^3 - 2yn - 5)/(3yn^2 - 2)
    = (2yn^3 + 5)/(3yn^2 - 2)

Thus, we have shown that the Newton-Raphson iterative formula for this function can be written as yn+1 = (2yn^3 + 5)/(3yn^2 - 2).

ii) Using the formula derived in part (i), we can find y1, y2, and y3 if y0 = 2 as follows:

y1 = (2y0^3 + 5)/(3y0^2 - 2)
  = (2 * 2^3 + 5)/(3 * 2^2 - 2)
  = (16 + 5)/(12 - 2)
  = **21/10**

y2 = (2y1^3 + 5)/(3y1^2 - 2)
  = (2 * (21/10)^3 + 5)/(3 * (21/10)^2 - 2)
  = **1.964**

y3 = (2y2^3 + 5)/(3y2^2 - 2)
  = (2 * (1.964)^3 + 5)/(3 * (1.964)^2 - 2)
  = **1.943**

Therefore, if y0 = 2, then y1 ≈ **21/10**, y2 ≈ **1.964**, and y3 ≈ **1.943** using the Newton-Raphson iterative formula.

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Answer:

m = 1/3

b = 1

Dashed

Below

Step-by-step explanation:

the average value of f(x) = 5x^2 over the interval [1,4] is 315/9, which can be simplified to 35/1 or simply 35.

To determine the average value of the function f(x) = 5x^2 over the interval [1,4], we need to calculate the definite integral of the function over the given interval and divide it by the length of the interval.

The average value of a function f(x) over the interval [a, b] is given by the formula:

(1 / (b - a)) * ∫[a to b] f(x) dx

In this case, we have f(x) = 5x^2 and the interval is [1,4]. Therefore, the average value of f(x) over the interval [1,4] is:

(1 / (4 - 1)) * ∫[1 to 4] 5x^2 dx

Evaluating the definite integral, we get:

(1 / 3) * [ (5/3)x^3 ] evaluated from x = 1 to x = 4

Substituting the limits into the expression, we have:

(1 / 3) * ( (5/3)(4^3) - (5/3)(1^3) )

Simplifying further, we get:

(1 / 3) * ( (5/3)(64) - (5/3)(1) )

= (1 / 3) * ( (320/3) - (5/3) )

= (1 / 3) * ( (320 - 5) / 3 )

= (1 / 3) * ( 315 / 3 )

= 315 / 9

Therefore, the average value of f(x) = 5x^2 over the interval [1,4] is 315/9, which can be simplified to 35/1 or simply 35.

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a. B(t) = 1.24t + 18.1;

b. Slope is 1.24, signifies increase in bottled water consumption per person every year;

c. Y-intercept is 18.1, signifies initial bottled water consumption per person in 2001.

a. To find the linear function, we need to first find the slope and y-intercept.

We can use the two given data points: (0, 18.1) and (10, 30.5).

Using the slope formula, we get:

slope = (30.5 - 18.1) / (10 - 0)

         = 1.24

Now we can use the point-slope form of a line to find the equation:

y - 18.1 = 1.24(t - 0)

y = 1.24t + 18.1

So the function is B(t) = 1.24t + 18.1.

b. The slope of the line is 1.24, which signifies that for every year since 2001, there is an increase in 1.24 gallons of bottled water consumed per person.

c. The y-intercept of the line is 18.1, which signifies the initial amount of bottled water consumed per person in 2001.

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Answer:

Just press 1 square because it is 1 out of 7

If the price level in Canada falls and the price level in the United States does not change, Canadian-manufactured sofas are relatively less expensive, so Sherri will likely purchase a Canadian manufactured sofa.

This is because the decrease in price level in Canada would make Canadian goods more affordable, including Canadian manufactured sofas. This makes them a more attractive option for Sherri than U.S. manufactured sofas which would still be relatively more expensive even if their price level did not change. Answer D is correct in this scenario. However, if U.S. manufactured sofas were initially more expensive than Canadian sofas, then answer B could also be correct. Overall, Sherri's decision would depend on the initial price difference between Canadian and U.S. manufactured sofas, as well as her personal preferences and any other relevant factors.

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Answer:

The nth term of the sequence will be:  n²/n+1

Step-by-step explanation:

Given the sequence

1/2 , 4/3 , 9/4 , 16/5

The values in the numerator are:

2, 3, 4, 5

It is clear that every successive value in the numerator can be determined by adding 1 to the previous value.

i.e.

3 = 2+1

4 = 3+1

5 = 4+1

Thus, the nominator contains the sequence rule: n+1

The values in the denominator are:

1, 4, 9, 16

It is clear that every value in the denominator is the square of the sequence number.

i.e.

1 = 1²

2 = 2²

3 = 3²

4 = 4²

5 = 5²

so

The denominator defines the rule n².

Thus, the nth term of the sequence will be:  n²/n+1

Answer:

2815 views

Step-by-step explanation:

Given :

⇒ Views on first day = 500

⇒ Rate of increase = 28%

============================================================

Creating a function :

⇒ Let y be the total number of views and x be the number of days since posted

⇒ y = 500 (1 + 0.28)ˣ = y = 500(1.28)ˣ

============================================================

Solving :

⇒ y = 500(1.28)⁷

⇒ y = 500(5.62949953)

⇒ y = 2815 views (nearest whole number)

Answer:

£94

Step-by-step explanation:

24+ (14×5) = £94

p.s pls give brainliest answer :)

since the population standard deviations (σ1 and σ2) are not provided, we cannot calculate the exact test statistic Z.

To test the null hypothesis H0: (μ1 - μ2) = 0 versus the alternative hypothesis Ha: (μ1 - μ2) ≠ 0, we can use a two-sample z-test. The test statistic is calculated as:

Z = (x bar1 - x bar2) / sqrt((σ1^2 / n1) + (σ2^2 / n2))

Where:
X bar1 and x bar2 are the sample means of the two groups,
σ1 and σ2 are the population standard deviations of the two groups,
n1 and n2 are the sample sizes of the two groups.

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Answer:

(-3)² = 9

Step-by-step explanation:

\((-3)^{-2} = \frac{1}{9}\)

Answer:

1/9

Step-by-step explanation:

(-3) ^ -2

The negative exponent means  a^-b = 1/a^b

1/(-3)^2

1/(-3*-3)

1/9

Answer:

The bottom one is correct

Step-by-step explanation:

Answer: Greater than the actual product

Step-by-step explanation: Trust

Answer:

24960(y-1)

I'm so glad to help you with this question hope you get it

Step-by-step explanation:

lateral surface area here = πrl

r = 10

l = √h²+r²= √ 24²+ 10² = 26

lateral surface area = 10 × 26 × π

= 260π in²

hope this will be helpful to you .

plz mark my answer as brainlist if you find it useful.

Answer:

The lateral area of cone is 260π in².

Step-by-step explanation:

\(\begin{gathered}\end{gathered}\)

\(\begin{gathered}\end{gathered}\)

\(\star{\underline{\boxed{\sf{\purple{\ell = \sqrt{{(r)}^{2} + {(h)}^{2}}}}}}}\)

\(\star{\underline{\boxed{\sf{\purple{La_{(Cone)}= \pi r\ell}}}}}\)

\(\begin{gathered}\end{gathered}\)

Finding the slant height of cone by substituting the values in the formula :

\(\begin{gathered} \qquad{\longrightarrow{\sf{\ell = \sqrt{{(r)}^{2} + {(h)}^{2}}}}}\\\\\qquad{\longrightarrow{\sf{\ell = \sqrt{{(10)}^{2} + {(24)}^{2}}}}}\\\\\qquad{\longrightarrow{\sf{\ell = \sqrt{{(10 \times 10)} + {(24 \times 24)}}}}}\\\\\quad{\longrightarrow{\sf{\ell = \sqrt{(100)+(576)}}}}\\\\\qquad{\longrightarrow{\sf{\ell = \sqrt{100 + 576}}}}\\\\\quad{\longrightarrow{\sf{\ell = \sqrt{676}}}}\\\\\quad{\longrightarrow{\sf{\ell = 26 \: in}}}\\\\\quad\star\underline{\boxed{\sf{\pink{\ell = 26 \: in}}}} \end{gathered}\)

Hence, the slant height of cone is 26 in.

\(\begin{gathered}\end{gathered}\)

Now, finding the lateral area of cone by substituting the values in the formula :

\(\begin{gathered} \qquad{\longrightarrow{\sf{La_{(Cone)} = \pi r \ell}}}\\\\\qquad{\longrightarrow{\sf{La_{(Cone)} = \pi \times 10 \times 26}}}\\\\\qquad{\longrightarrow{\sf{La_{(Cone)} = \pi \times 260}}}\\\\\qquad{\longrightarrow{\sf{La_{(Cone)} = 260\pi\: {in}^{2}}}}\\\\ \qquad{\star{\underline{\boxed{\sf{\pink{La_{(Cone)} = 260\pi \: {in}^{2}}}}}}}\end{gathered}\)

Therefore, the lateral area of cone is 260π in².

\(\rule{300}{2.5}\)

The quadratic inequality defined on the graph is given as follows:

y ≥ 2/3(x + 3)² - 24.

The coordinates of the vertex of the quadratic function are given as follows:

(-3, -24).

Hence the quadratic function is given as follows:

y = a(x + 3)² - 24.

In which a is the leading coefficient.

When x = 3, y = 0, hence the leading coefficient a is obtained as follows:

0 = a(3 + 3)² - 24

36a = 24

a = 24/36

a = 2/3.

Hence:

y = 2/3(x + 3)² - 24.

The quadratic function has a solid curve, and the values above it are pained, hence the inequality is given as follows:

y ≥ 2/3(x + 3)² - 24.

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The expression with its given values. 3x/y ; x = 4, y = 12 is 1

Given expression= 3x/y

x= 4 and y= 12

putting the values of x and y in the given expression,

3*4/12 = 1

The answer for the given expression is 1.

What is an Expression?

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Answer:

Percentage: 115%

Decimal: 1.15

Fraction: \(\frac{23}{20}\\\)

Step-by-step explanation:

Percentages, Fractions, and Decimals

Assume we set 100% as the original price of the food that Michael consumed. When he leaves a 15% tip for the waitress, he is really paying 100%+15%=115% of the original price.

Now we express 115% as a decimal, simply dividing by 100:

115% = 115/100 = 1.15

To express it as a fraction, we simplify the division instead of calculating it:

115% = \(\frac{115}{100}\)

Simplifying by 5:

115% = \(\frac{23}{20}\)

The graph of a proportional relationship is a line through the origin or a ray whose endpoint is the origin

3. No because it's a line that doesn't go through the origin

4. Yes because it's a line through the origin

5. Yes because 1/3 = 2/6 = 3/9 = 4/12

6. No because 4/2 isn't equal to 8/5

7. Draw a graph just like 4., but change the y-axis

8. a. Let the equation be y = ax. 27 = 3a. a = 9. Therefore the equation is y = 9x.

8. b. 9

8. c. 9 * 5 = 45

9. a. The car travels 25 (> 18) miles per gallon of gasoline.

9. b. 25 * 8 - 18 * 8 = 7 * 8 = 56

The meaning of the graph of the earnings for Popsicle Palace after x months is given as follows:

The first step in interpreting the graph is identifying the variables on the graph, as follows:

Then the graph describes the earnings as a function of the month, and we just have to describe if the earnings are increasing or decreasing.

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Answer:

37

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

8x + 15 = 5.5x +25

so 2.5x =10

x=4

The complete table of the function is:

\(\begin{array}{cccccccc}x & {0} & {1} & {2} & {3} & {4}& {5} & {6} \ \\ f(x) & {72} & {60} & {48} & {36} & {24}& {12} & {0} \ \end{array}\)

The equation missing from the question is:

\(y = 72 - 12x\)

To complete the table, we simply calculate the y value for each x value;

When \(x = 0\),     \(y = 72 - 12 * 0 = 72\)

When \(x = 1\),     \(y = 72 - 12 * 1 = 60\)

When \(x = 2\),     \(y = 72 - 12 * 2 = 48\)

When \(x = 3\),     \(y = 72 - 12 * 3 = 36\)

When \(x = 4\),     \(y = 72 - 12 * 4 = 24\)

When \(x = 5\),     \(y = 72 - 12 * 5 = 12\)

When \(x = 6\),     \(y = 72 - 12 * 6 = 0\)

So, the complete table is:

\(\begin{array}{cccccccc}x & {0} & {1} & {2} & {3} & {4}& {5} & {6} \ \\ f(x) & {72} & {60} & {48} & {36} & {24}& {12} & {0} \ \end{array}\)

To create a graph of f(x), we simply type \(y = 72 - 12x\) on a drawing tool and the graph will be generated.

See attachment for graph

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Answer:

Step-by-step explanation:

Answer:

2920

Step-by-step explanation: