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Based on the triangle midsegment theorem, the length of CZ is calculated as: 7.2 m.

The triangle midsegment theorem states that when two sides of a triangle are joined together by a line segment at their midpoint, the line segment is called the midsegment, and it is parallel to the third side whose measure is twice its length.

This implies that, AB is a midsegment in the image shown for triangle XYZ. It is parallel to YZ.

Therefore:

AB = 1/2(the length of YZ)

Substitute the value of AB into the equation:

7.2 = 1/2(YZ)

2(7.2) = YZ

YZ = 14.4 m.

The length of CZ = 1/2(the length of YZ) [this is because YC = CZ]

CZ = 1/2(14.4)

CZ = 7.2 m.

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The 95% confidence interval for the true proportion of all auto accidents involving teenage drivers is approximately (0.1205, 0.1927).

To find the 95% confidence interval for the true proportion of all auto accidents involving teenage drivers, we can use the formula for the confidence interval for a proportion.

The formula for the confidence interval is:

CI = p1 ± Z * √((p1 * (1 - p1)) / n)

Where:

CI is the confidence interval,

p1 is the sample proportion (proportion of accidents involving teenage drivers),

Z is the Z-score corresponding to the desired confidence level (95% confidence level corresponds to Z ≈ 1.96),

n is the sample size (number of accidents checked).

Given:

Number of accidents checked (sample size), n = 582

Number of accidents involving teenage drivers, x = 91

First, we calculate the sample proportion:

p1 = x / n = 91 / 582 ≈ 0.1566

Now we can calculate the confidence interval:

CI = 0.1566 ± 1.96 * √((0.1566 * (1 - 0.1566)) / 582)

Calculating the standard error of the proportion:

SE = √((p1 * (1 - p1)) / n) = √((0.1566 * (1 - 0.1566)) / 582) ≈ 0.0184

Substituting the values into the formula:

CI = 0.1566 ± 1.96 * 0.0184

Calculating the values:

CI = 0.1566 ± 0.0361

Finally, we can simplify the confidence interval:

CI = (0.1205, 0.1927)

Therefore, the 95% confidence interval for the true proportion of all auto accidents involving teenage drivers is approximately (0.1205, 0.1927).

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Answer:

5.6ft squared

Step-by-step explanation:

4x7 = 28 divided by 5 which is 5.6

Using the given fractions if the abominable snowman has six snow cones and has already eaten 1/3 of them, there are four snow cones left for him to give to Mike.

To solve this problem, we need to subtract the number of snow cones that the abominable snowman has already eaten from the total number of snow cones that he started with.

If the abominable snowman started with six snow cones and already ate 1/3 of them, then we need to find 1/3 of 6 to determine how many snow cones he has already eaten:
1/3 x 6 = 2

So, the abominable snowman has already eaten two snow cones.

To find out how many snow cones are left, we subtract 2 from the total number of snow cones:
6 - 2 = 4

Therefore, there are four snow cones left that the abominable snowman can give to Mike.

In summary, if the abominable snowman has six snow cones and has already eaten 1/3 of them, there are four snow cones left for him to give to Mike.

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Answer:

Question not properly explained

Answer:

Step-by-step explanation:

To find g[f(2)], we need to evaluate the composite function g[f(2)] by first finding f(2) and then substituting the result into g(x).

Let's start by finding f(2):

f(x) = 2x² - 3x

f(2) = 2(2)² - 3(2)

= 2(4) - 6

= 8 - 6

= 2

Now that we have the value of f(2) as 2, we can substitute it into g(x):

g(x) = 5x - 1

g[f(2)] = g(2)

= 5(2) - 1

= 10 - 1

= 9

Therefore, g[f(2)] is equal to 9.

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Answer:

It is wrong

Step-by-step explanation:

What we have is as follows;

9x + 2 = 8x^2 + 6x

Bringing 9x + 2 yo the right hand side, we have;

8x^2 + 6x -9x -2 = 0

8x^2 -3x -2 = 0

So what is used here is the quadratic formula and we want to try to see if it was used correctly.

The form we have in the question is however;

-8x^2+ 3x + 2 = 0

which is obtained by taking the right hand side of the equation to the left

Now;

using the quadratic formula;

x = -b ± √(b^2 -4ac)/2a

where a is -8

b = 3

c = 2

Thus we have

-3 ± √(9 - 4(-8)2)/2(-8)

-3 ± √(9 + 64)/(-16)

So where is wrong is in the square root

what we are supposed to have is 9 + 64 = 73 and not otherwise

Answer:

Step-by-step explanation:

No. The correct values of a, b, and c were substituted in, but the formula was simplified wrong. The 64 should be added so the radicand is 73. There should be 2 real roots.

Answer:

u(-2;2)

Step-by-step explanation:

Answer:

y= -3x + 20

Step-by-step explanation:

just graph it out

Answer:

(4m - 1) × (2n + n)

Step-by-step explanation:

8m - 2 + 4mn - n

2(4m - 1) + 4mn - n

2(4m - 1) + n × (4m - 1)

= (4m - 1) × (2n + n)

The answer is (4m - 1) × (2n + n)

The simplest way of factorizing is:

Factorise: 8m-2+4mn-n

⇒ 8m - 2 + 4mn - n

⇒ 2(4m - 1) + 4mn - n

⇒ 2(4m - 1) + n × (4m - 1)

⇒ (4m - 1) × (2n + n)

Factorising is a way of writing an expression as a product of its factors using brackets.

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With the help of the figure we can say that triangles are congruent by SAS Rule

What is Congruence of Triangle?

Triangle congruence: Two triangles are said to be congruent if all three of their corresponding sides are equal and all three of their corresponding angles are equal in size. These triangles can be moved, rotated, flipped, and turned to look exactly the same.

Solution:

By SAS rule, two triangles are said to be congruent if any two sides and the angle included between the sides of one triangle are comparable to the corresponding two sides and the angle included between the sides of the second triangle.

In given figure, sides AB= PQ, BC=QR and angle between AB and BC equal to angle between PQ and QR i.e. ∠B = ∠Q. Hence, Δ ABC ≅ Δ PQR.

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Slope can be found using the following equation:

slope (m) = \(\frac{y_2 - y_1}{x_2 - x_1}\)

7) Let:

\((x_1 , y_1) = (-1 , -11)\\(x_2 , y_2) = (-6 , -7)\)

Plug in the corresponding numbers to the corresponding variables:

m = \(\frac{-7 - (-11)}{-6 - (-1)} = \frac{-7 + 11}{-6 + 1} = \frac{4}{-5} = -\frac{4}{5}\)

Slope: \(-\frac{4}{5}\)

8) Let:

\((x_1 , y_1) = (-7 , -13)\\(x_2 , y_2) = (1 , -5)\)

Plug in the corresponding numbers to the corresponding variables:

m = \(\frac{-5 - (-13)}{1 - (-7)} = \frac{-5 + 13}{1 + 7} = \frac{8}{8} = 1\)

Slope: \(1\)

9) Let:

\((x_1 , y_1) = (-5 , 3)\\(x_2 , y_2) = (8 , 3)\)

Plug in the corresponding numbers to the corresponding variables:

m = \(\frac{3 - (3)}{8 - (-5)} = \frac{0}{8 + 5} = \frac{0}{13} = 0\)

Slope: \(0\)

10) Let:

\((x_1 , y_1) = (3 , -2)\\(x_2 , y_2) = (15 , 7)\)

Plug in the corresponding numbers to the corresponding variables:

m = \(\frac{7 - (-2)}{15 - 3} = \frac{7 + 2}{15 - 3} = \frac{9}{12}\)

Simplify the slope. Divide common factors from both the numerator and denominator:

\((\frac{9}{12})/(\frac{3}{3} ) = \frac{3}{4}\)

Slope: \(\frac{3}{4}\)

11) Let:

\((x_1 , y_1) = (-5 , -10)\\(x_2 , y_2) = (-5 , -1)\)

Plug in the corresponding numbers to the corresponding variables:

m = \(\frac{-1 - (-10)}{-5 - (-5)} = \frac{-1 + 10}{-5 + 5} = \frac{9}{0} =\) undefined.

Slope: undefined

12) Let:

\((x_1 , y_1) = (-4 , -2)\\(x_2 , y_2) = (-12, 16)\)

Plug in the corresponding numbers to the corresponding variables:

m = \(\frac{16 - (-2)}{-12 - (-4)} = \frac{16 + 2}{-12 + 4} = \frac{18}{-8} = -\frac{18}{8} = ((-\frac{18}{8})/( \frac{2}{2}) = -\frac{9}{4}\)

Slope: \(-\frac{9}{4}\)

~

Answer:

1) I believe the answer is D

Explanation: The square root of 7 is approximately 2.64 which then gets divided by 3 which results in approximately 0.88, then you have to factor in that the problem has only one negative sign; therefore, the answer should be Point D.

Step-by-step explanation:

For the second one turn them into decimals

5/8 = 0.625

2√5 = 4.472

-pi/3 = -1.047

Then rearrange them 2√5, 5/8, -pi/3

Answer:

x = 2, x = 8

Step-by-step explanation:

reminder that f'(x) = \(m_{tangent}\)

Differentiate f(x) term by term using the power rule

\(\frac{d}{dx}\) (a\(x^{n}\) )  = na\(x^{n-1}\)

f(x) = \(\frac{1}{3}\) x³ - 5x² + 2x + 10

f'(x) = x² - 10x + 2

Equating f'(x) to - 14

x² - 10x + 2 = - 14 ( add 14 to both sides )

x² - 10x + 16 = 0 ← in standard form

(x - 2)(x - 8) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 2 = 0 ⇒ x = 2

x - 8 = 0 ⇒ x = 8

Answer:(-1,1) - (4,4)

Step-by-step explanation:

ez

The correct option is a) (x + y) (y + z). Given the output function F in sum-of-minterms form as F = (0, 1, 2, 3, 7), we need to determine the corresponding Boolean expression for the output function.

A 3x8 decoder has three input variables (x, y, z) and eight output variables, where each output variable corresponds to a unique combination of input variables. The output variables are typically represented as minterms.

Let's analyze the given output function F = (0, 1, 2, 3, 7). The minterms represent the outputs that are equal to 1. By observing the minterms, we can deduce the corresponding Boolean expression.

From the minterms, we can see that the output is equal to 1 when x = 0, y = 0, z = 0 or x = 0, y = 0, z = 1 or x = 0, y = 1, z = 0 or x = 0, y = 1, z = 1 or x = 1, y = 1, z = 1.

By simplifying the above conditions, we get (x + y) (y + z), which is the Boolean expression corresponding to the given output function F.

In summary, the correct option is a) (x + y) (y + z).

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0² = 0 ( zero to the power of any no. equals to zero )

0-² = 1/0² = 1/0 ( numerator can't be zero , it's undefined )

0⁰ is undefined

Skills

a) P² × P⁵ = P⁷

b)P¹²÷P⁴ = P³

c) (P³)⁷ = P²¹

d) P⁰× q³ = 1 × q³ = q³

e) 3P⁴×5P² = 15P⁶

f) 6Pq³×2P⁹q² = 12P¹⁰q⁵

g)P⁷/P² = P⁵

h)8P¹¹/2P⁹ = 4P²

i) (2P⁴)³=2³×P¹² = 8P¹²

j) (8q²×3q⁷)/6q⁸ = 24q⁹/6q⁸ = 4q

Stretch

a) 2²⁰÷4¹⁰= 1048576÷1048576 = 1

b) (2⁶)²÷4⁵ = 2¹²÷4⁵ = 4096 ÷ 1024 = 4

c) 3⁷ ÷ 9³ = 2187 ÷ 729 = 3

d) 27⁵ ÷ 3¹² = 14348907 ÷ 531441 = 27

Please give brainliest

\(\textsf {Skills :}\)

\(\mathsf {a) p^{2} \times p^{5} = p^{7}}\)

\(\mathsf {b) p^{12} \div p^{4} = p^{8}}\)

\(\mathsf {c) (p^{3})^{7} = p^{21}}\)

\(\mathsf {d) p^{0} \times q^{3} = q^{3}}\)

\(\mathsf {e) 3p^{4} \times 5p^{2} = 15p^{6}}\)

\(\mathsf {f) 6pq^{3} \times 2p^{9}q^{2} = 12p^{10}q^{5}}\)

\(\mathsf {g)\frac{p^{7}}{p^{2}} = p^{5}}\)

\(\mathsf {h) \frac{8p^{11}}{2p^{9}}=4p^{2}}\)

\(\mathsf {i) (2p^{4})^{3} = 8p^{12}}\)

\(\mathsf {j) \frac{8q^{2} \times 3q^{7}}{6q^{8}} = 4q}\)

\(\textsf {Stretch :}\)

\(\mathsf {a) 2^{20} \div 4^{10} = 2^{20} \div 2^{20} = 1}\)

\(\mathsf {b) (2^{6})^{2} \div 4^{5} = 2^{12} \div 2^{10} = 2^{2} = 4}\)

\(\mathsf {c) 3^{7} \div 9^{3} = 3^{7} \div 3^{6} = 3}\)

\(\mathsf {d) 27^{5} \div 3^{12} = 3^{15} \div 3^{12} = 3^{3} = 27}\)

Using the combination formula, it is found that there are 220 ways to decide which countries to skip.

The order in which the countries are skipped is not important, hence the combination formula is used to solve this question.

\(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by:

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

In this problem, 3 countries are skipped from a set of 12, hence the number of ways is given by:

\(C_{12,3} = \frac{12!}{3!9!} = 220\)

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The domain of  the composition function fog(x) when f(x)= √6x and g(x)= 1/ (x-6) is equal to  (-∞, 6) U (6, ∞).

Function f(x) = √6x

And g(x)= 1/ (x-6

Composition function fog is ,

fog(x) = f(g(x))

Domain of fog(x),

First, find the domain of g(x),

Here,

g(x) = 1/(x-6)

The denominator of g(x) cannot be equal to zero,

So we must exclude x = 6 from the domain of g(x).

The domain of g(x) is equal to ,

domain of g(x) = {x | x ≠ 6}

The range of g(x) is,

As x approaches 6 from the left, g(x) approaches negative infinity,

And as x approaches 6 from the right, g(x) approaches positive infinity.

Range of g(x) = (-∞, 0) U (0, ∞)

Now, the domain of fog(x),

fog(x)

= f(g(x))

= √6g(x)

=√ 6 (1 /(x - 6 ) )

Square root sign must be non-negative.

Since the range of g(x) does not include zero,

Exclude the part of the range that is less than zero.

The domain of fog(x) is,

domain of fog(x)

= {x | g(x) > 0}

= {x | x < 6} U {x | x > 6}

The domain of fog(x) consists of all real numbers except x = 6.

Therefore, the domain of fog(x) is (-∞, 6) U (6, ∞).

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The above question is incomplete, the complete question is :

Given f(x)= √6x and g(x)= 1/ (x-6) Which value is in the domain of fog.

Answer:

Lets take all factors into consideration first

The door is a rectangle and the area of a rectangle is length times width

Let the width be w

Let the length be l

Equation length × breadth = area

(w+48)w = 3024

w^2 + 48w = 3024

w^2 + 48w - 3024 = 0

w^2 + 84w - 36w - 3024 = 0

w(w + 84) -36 ( w + 84) = 0

(w + 84) (w - 36) = 0

w + 84 = 0 AND w - 36 =0

w = -84 and w = 36

Since width cannot be negative, the right answer is 36

How did I get 84 and 36? Well, I had to factorize 3024 and since 84 times 36 is 3024 and 84 minus 36 is 48, I chose them.

The statement is true. Roofs with a span of 40 feet or less and a pitch of ? or greater, as well as roofs with a span of more than 40 feet and a pitch of 1/4 or greater, are considered to be pitched.

In roofing terminology, the pitch refers to the steepness or slope of a roof. A pitched roof has a slope that allows water to drain efficiently. The pitch is typically measured as a ratio of vertical rise to horizontal span.

According to the statement, roofs with a span of 40 feet or less and a pitch of ? (undefined or not specified) or greater are considered to be pitched. This means that as long as the roof has a certain degree of slope or steepness, it is categorized as a pitched roof.

Similarly, roofs with a span of more than 40 feet and a pitch of 1/4 or greater are also considered to be pitched. In this case, the requirement for a minimum pitch of 1/4 (or a steeper slope) applies to roofs with a larger span.

The classification of roofs as pitched or not pitched depends on their span and the minimum pitch requirements specified. Roofs that meet the specified criteria for span and pitch are considered to be pitched roofs.

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The value that will be returned by the function if the values of x and y are 4 and 10 is 54.

The given code snippet is a CPP code to find the sum of the two parameters that are given as input in the parameter.

The given function operatenum takes two integer arguments x and y. It calculates the sum of x and y and assigns it to the variable s, then calculates the product of x and y and assigns it to the variable p. Finally, it returns the sum s concatenated with the product p.

int operatenum(int x, int y) {       \\x and y are the parameter

   int s, p;                                     \\ local variable

   s = x + y;                                   \\ s stores the sum of the variable x and y

   p = x * y;                                   \\ p stores the product of x and y

   return (s + p);                            \\ the function returns the sum of s and p

}

so after executing the code by passing 4 and 10 as the values of x and y respectively:

s= 4+10=14

p=4*10=40

the return statement returns (s*p) which is 14+40= 54.

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Selling price = $6.37 .

Selling price = $6.94

Selling price = $346.80

1)

Sales revenue = 6,000

Less:-Variable costs ($1.5 per unit 1,000) = 1,500

Less:- Fixed costs = (1,700)

Operating Income = 2,800

Variable costs and Fixed costs have increased.

Hence, in order to maintain the same Operating Income, the selling price should be higher than the current selling price .

Thus to maintain same operating income the selling price should be $6.37 .

2)

The computation is given below:

Sales price = ( Total sales revenue ÷ packages sold)

Total sales revenue = ( Total Cost + Operating income )

Total Cost = ( Variable Cost + Fixed cost)

Now

Variable cost = 1,000 packages × $1.90 per unit

= $1,900

Fixed cost = $1,700 × 120%

= $2040

Total cost = $1,900 + $2,040

= $3,940

Now  

Total sales revenue is

= $3,940 + $3,000

= $6,940

Now  

Sales price = $6,540 ÷ 1,000 packages

= $6.94

3)

-Fruit Computer Company has variable costs of $220 per unit and fixed costs of $32,000 per month.

- The company currently sells 500 units per month at a sales price of $300.

Net margin = $8000

- The company wants to increase its operating income by 30%.

- If the company upgrades the computer quality, the variable cost per unit will increase to $240 and the fixed costs will rise by 50%.

Thus the selling price per unit will be  $346.80 per unit.

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Answer:

\(x=-3\)

Answer:

x=3

Step-by-step explanation:

-6x+2=-5x+5

        +5x .    +5x

             -2 .-2

        -1 .   -1

Answer:

The slope is 1/3

56/120

Step-by-step explanation:

The body masses of the two children in terms of their father's body mass, x, are:

First child's body mass = 5x/6 kg

Second child's body mass = 4x/5 kg

To express the body mass of the man's two children in terms of their father's body mass, we can use the given ratios.

Let the body mass of the man be x kg.

The first child's body mass is five-sixths of their father's body mass:

Body mass of the first child = (5/6) * x

= 5x/6 kg.

The second child's body mass is four-fifths of their father's body mass:

Body mass of the second child = (4/5) * x

= 4x/5 kg.

Therefore, the body masses of the two children in terms of their father's body mass, x, are:

First child's body mass = 5x/6 kg

Second child's body mass = 4x/5 kg

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Answer:

1 is 9 sq units

2 is 12

3 is 24cm^2

Step-by-step explanation: