How far from the base of the house do you need to place a 13-foot ladder so that it exactly reaches the top of a 10-feet wall?

Answer:

[tex]\sqrt{51}[/tex] units.

Step-by-step explanation:

Point E is inside a rectangle ABCD.

Please refer to the attached image for the given statement and dimensions.

Given that:

Sides AE = 6 units

BE = 7 units and

CE = 8 units

To find:

DE = ?

Solution:

For a point E inside the rectangle the following property hold true:

[tex]AE^2+CE^2=BE^2+DE^2[/tex]

Putting the given values to find the value of DE:

[tex]6^2+8^2=7^2+DE^2\\\Rightarrow 26+64=49+DE^2\\\Rightarrow DE^2=100-49\\\Rightarrow DE^2=51\\\Rightarrow \bold{DE = \sqrt{51}\ units}[/tex]

Answer:

2000

Step-by-step explanation:

20,000 is 2000 times the number 10.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given numbers are 20000 and 10. The number 20000 is how many times the number 10 will be calculated by dividing the number 20000 by 10.

E = 20000 / 10 = 2000

Therefore, the number 20,000 is 2000 times the number 10.

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[tex]|\Omega|=2\cdot6=12\\|A|=1\cdot2=2\\\\P(A)=\dfrac{2}{12}=\dfrac{1}{6}[/tex]

Answer:

Step-by-step explanation:

Given that:

Let sample size of women be [tex]n_1[/tex]  = 1000

Let the proportion of the women be [tex]p_1[/tex] = 0.65

Let the sample size of the men be [tex]n_2[/tex] = 1000

Let the proportion of the mem be [tex]p_2[/tex]  = 0.60

The null and the alternative hypothesis can be computed as follows:

[tex]H_0: p_1 = p_2[/tex]

[tex]H_0a: p_1 \neq p_2[/tex]

Thus from the alternative hypothesis we can realize that this is a two tailed test.

However, the pooled sample proportion p = [tex]\dfrac{p_1n_1+p_2n_2 } {n_1 +n_2}[/tex]

p =[tex]\dfrac{0.65 * 1000+0.60*1000 } {1000 +1000}[/tex]

p = [tex]\dfrac{650+600 } {2000}[/tex]

p = 0.625

The standard error of the test can be computed as follows:

[tex]SE = \sqrt{p(1-p) ( \dfrac{1} {n_1}+ \dfrac{1}{n_2} )}[/tex]

[tex]SE = \sqrt{0.625(1-0.625) ( \dfrac{1} {1000}+ \dfrac{1}{1000} )}[/tex]

[tex]SE = \sqrt{0.625(0.375) ( 0.001+0.001 )}[/tex]

[tex]SE = \sqrt{0.234375 (0.002)}[/tex]

[tex]SE = \sqrt{4.6875 * 10^{-4}}[/tex]

[tex]SE = 0.02165[/tex]

The test statistics is :

[tex]z =\dfrac{p_1-p_2}{S.E}[/tex]

[tex]z =\dfrac{0.65-0.60}{0.02165}[/tex]

[tex]z =\dfrac{0.05}{0.02165}[/tex]

[tex]z =2.31[/tex]

At level of significance of 0.05  the critical value for the z test will  be in the region between - 1.96 and 1.96

Rejection region: To reject the null hypothesis if z < -1.96 or z > 1.96

Conclusion: Since the value of z is greater than 1.96, it lies in the region region. Therefore we reject the null hypothesis and we conclude that  the percentage of men and women favoring a higher legal drinking age is different.

Answer:

Length = 21.3333333333;   Width: 12.6666666667

Step-by-step explanation:

Perimeter = 68

Perimeter of a rectangle:

2 (L +W)

Length (L) = 2W - 4

Width = W

2 ( 2W -4 +W) = 68

=> 2 (3W - 4) = 68

=> 6w -8 = 68

=> 6w = 76

=> w = 12.6666666667

Length = (12.6666666667 X 2) - 4

=> 21.3333333333

Answer:

2·5·5·5·5

Step-by-step explanation:

2(5)^4 is equivalent to 2·5·5·5·5; 2 is used as a multiplicand just once, but 5 is used four times.

Answer:

The percentage is  k  =  2.3%

Step-by-step explanation:

From the question we are told that

  The  population mean is  [tex]\mu = 47[/tex]

    The  standard deviation is  [tex]\sigma = 14[/tex]

Given that the sales are normally distributed and that students at a certain school who sell at least 75 magazine subscriptions win a prize then the  percent of the fourth grade students receive a prize is mathematically represented as

     [tex]P(X > 75) = P(\frac{X - \mu }{\sigma } > \frac{75 - \mu }{\sigma })[/tex]

Generally

     [tex]\frac{X - \mu }{\sigma } = Z (The \ standardized \ value \ of \ X )[/tex]

So

   [tex]P(X > 75) = P(Z > \frac{75 - 47 }{14 })[/tex]

   [tex]P(X > 75) = P(Z > 2)[/tex]

From the standardized normal distribution table  

      [tex]P(Z > 2) =0.023[/tex]

=>   [tex]P(X > 75) = 0.023[/tex]

The  percentage of the fourth grade students receive a prize is  

  k =  0.023 * 100

   k  =  2.3%

[tex]f(x)=18(0.8)=14.4[/tex]

is a constant function, so it will be a straight line parallel to x axis and passing through y axis at $14.4$

Answer:

It rotated 180 degrees

Step-by-step explanation:

If you use this image and paste in on to google docs you will be able to rotate the image. Use this tool so that your can identify the amount of degrees.

If the Quadrilateral A'B'C'D' is the image of quadrilateral ABCD under a rotation about the origin, (0,0) then the angle of rotation is option (c) 180 degrees

In geometry a quadrilateral is a four-sided polygon, having four edges and four corners

The angle of rotation is a measurement of the amount, of namely angle, that a figure is rotated about a fixed point, often the center of a circle.

Given,

Quadrilateral A'B'C'D' is the image of quadrilateral ABCD under a rotation about the origin, (0,0)

Consider the coordinates of D and D'

D(2,3) and D'(-2,-3)

Connect D and D'

∠D0D' = 180 Degrees

Hence, If the Quadrilateral A'B'C'D' is the image of quadrilateral ABCD under a rotation about the origin, (0,0) then the angle of rotation is option (c) 180 degrees

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Answer:

3x^2

Step-by-step explanation:

3 x times the fraction 1 over x to the power of negative 4 => 3x * 1/x^-4

= 3x *x^4 = 3x^5

times x to the power of negative 3 => x^-3

3x^5 * x^-3 = 3x^2

Answer:

3x^2

Step-by-step explanation:

i got it right on the test on god!

[tex]x^2-3x+2=0\\x^2-x-2x+2=0\\x(x-1)-2(x-1)=0\\(x-2)(x-1)=0\\x=2 \vee x=1\\\\x^2=4 \vee x^2=1[/tex]

Answer:

Step-by-step explanation:

First we try to factor x²-3x+2.

We have to look for two numbers that multiply to 2 and add -3.

The two numbers are -1 and -2.

(x-1)(x-2) = 0

x-1 = 0 -> x = 1

x-2 = -> x = 2

Now we find x^2.

(1)^2 = 1

(2)^2 =4

Answer:

240 candidates

Step-by-step explanation:

40% candidates failed, i. e. out of every 100 candidates 40 failed.

40 failed ----------------------------- 100 total students

1 failed --------------------------------100/40 total students, given 160 failed therefore

160 failed ----------------------------(100/40) x 160 total students

Total students = (100/40) x 160 = 400

Number of candidates passed = (total candidates) - (total candidates failed)

                                                   = 400 - 160 = 240 candidates

Answer:

The range of the function f(x)= (x-4)(x-2) is all real numbers greater than or equal to -1

Step-by-step explanation:

Hi there! :)

Answer:

[tex]\huge\boxed{m = \frac{3}{2}}[/tex]

Find the slope using the slope formula:

[tex]m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Plug in the coordinates of each point:

[tex]m = \frac{-1 - (-4)}{3 - 1}[/tex]

Simplify:

[tex]m = \frac{3}{2}[/tex]

Therefore, the slope of the line is 3/2.

Answer:

3/2

Step-by-step explanation:

The slope is given by

m = (y2-y1)/(x2-x1)

    = ( -1 - -4)/(3-1)

     = ( -1+4)/(2)

     = ( 3/2)

Answer:

20000 kg

Step-by-step explanation:

Recall that 1 kg = 2.2 lb approximately.  Then:

22 tons        1 kg        2000 lb

------------ * ------------ * --------------  =  20000 kg

      1           2.2 lb          1 ton

Answer:

t = (448 hrs/ week) / (30 hrs / week)

Step-by-step explanation:

Number of times park opens in a week = 7

Number of ticket booth = 8

Opening hours = 10am - 6pm = 8 hours per day

Max working hours per ticket seller per week = 30 hours

Therefore each booth works for 8 hours per day,

Then ( 8 * 7) = 56 hours per week.

All 8 booths work for (56 * 8) = 448 hours per week

If Max working hours per ticket seller per week = 30 hours,

Then muninim number of workers required (t) :

Total working hours of all booth / maximum number of working hours per worker per week

t = (448 hrs/ week) / (30 hrs / week)

Answer:

48082464 is the answer

Step-by-step explanation:

=[(116)3×114] × 1212​

=[348×114] × 1212

=39672 × 1212

=48082464 is the answer

hope it will help :)

Hey There!!

All you really need To do is: Divide [(116)] 3 x 114] x 1212) ( 20 + 51 + 43) ÷ 7

Hope It Helped!~ ♡

ItsNobody~ ☆

Answer:

[tex]\frac{x^{\frac{5}{6}} }{x^{\frac{1}{6}} } = x^{(\frac{5}{6} -\frac{1}{6}) }= x^{\frac{4}{6} }\\\sqrt{x} . \sqrt[4]{x} = x^{\frac{1}{2} } . x^{\frac{1}{4} } = x^{(\frac{1}{2} +\frac{1}{4}) } = x^{\frac{3}{4}[/tex]

The can be divided into two rectangles, one having length [tex]8.3[/tex] and width $3.8$

Another with, dimensions $7.4-3.8=3.6$ and $3.9$

Area of first rectangle=$3.8\times8.3=31.54$

Area of second rectangle =$3.6\times3.9=14.04$

Total area $=31.54+14.04=45.58$ ft²

Answer:

45.58 ft^2

Step-by-step explanation:

We can split the figure into two pieces

We have a tall rectangle that is 3.8 by 8.3

A = 3.8 * 8.3 =31.54 ft^2

We also have a small rectangle on the right

The dimensions are ( 7.4 - 3.8) by 3.9

A = 3.6*3.9 =14.04 ft^2

Add the areas together

31.54+14.04

45.58 ft^2

Answer:

Option b. None is the correct option.

The Answer is 63%

Step-by-step explanation:

To solve for this question, we would be using the z score formula

The formula for calculating a z-score is given as:

z = (x-μ)/σ,

where

x is the raw score

μ is the population mean

σ is the population standard deviation.

We have boxes X and Y. So we will be combining both boxes

Mean of X = 100 lb

Mean of Y = 5 lb

Total mean = 100 + 5 = 105lb

Standard deviation for X = 1 lb

Standard deviation for Y = 0.5 lb

Remember Variance = Standard deviation ²

Variance for X = 1lb² = 1

Variance for Y = 0.5² = 0.25

Total variance = 1 + 0.25 = 1.25

Total standard deviation = √Total variance

= √1.25

Solving our question, we were asked to find the percent of filled boxes weighing between 104 lb and 106 lb are to be expected. Hence,

For 104lb

z = (x-μ)/σ,

z = 104 - 105 / √25

z = -0.89443

Using z score table ,

P( x = z)

P ( x = 104) = P( z = -0.89443) = 0.18555

For 1061b

z = (x-μ)/σ,

z = 106 - 105 / √25

z = 0.89443

Using z score table ,

P( x = z)

P ( x = 106) = P( z = 0.89443) = 0.81445

P(104 ≤ Z ≤ 106) = 0.81445 - 0.18555

= 0.6289

Converting to percentage, we have :

0.6289 × 100 = 62.89%

Approximately = 63 %

Therefore, the percent of filled boxes weighing between 104 lb and 106 lb that are to be expected is 63%

Since there is no 63% in the option, the correct answer is Option b. None.

The percent of filled boxes weighing between 104 lb and 106 lb is to be expected will be 63%.

It is also called the Gaussian Distribution. It is the most important continuous probability distribution. The curve looks like a bell, so it is also called a bell curve.

The z-score is a numerical measurement used in statistics of the value's relationship to the mean of a group of values, measured in terms of standards from the mean.

A machine fills boxes weighing Y lb with X lb of salt, where X and Y are normal with a mean of 100 lb and 5 lb and standard deviation of 1 lb and 0.5 lb, respectively.

The percent of filled boxes weighing between 104 lb and 106 lb is to be expected will be

Then the Variance will be

[tex]Var = \sigma ^2[/tex]

Then for X, we have

[tex]Var (X) = 1^2 = 1[/tex]

Then for Y, we have

[tex]Var (Y) = 0.5^2 = 0.25[/tex]

Then the total variance will be

[tex]Total \ Var (X+Y) = 1 + 0.25 = 1.25[/tex]

The total standard deviation will be

[tex]\sigma _T = \sqrt{Var(X+Y)}\\\\\sigma _T = \sqrt{1.25}[/tex]

For 104 lb, then

[tex]z = \dfrac{104-105}{\sqrt{25}} = -0.89443\\\\P(x = 104) = 0.18555[/tex]

For 106 lb, then

[tex]z = \dfrac{106-105}{\sqrt{25}} = 0.89443\\\\P(x = 106) = 0.81445[/tex]

Then

[tex]P(104 \leq Z \leq 106) = 0.81445 - 0.18555 = 0.6289 \ or \ 62.89\%[/tex]

Approximately, 63%.

More about the normal distribution link is given below.

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Answer:

3 years

Step-by-step explanation:

Use the formula I = prt, where I is the interest money made, p is the starting amount of money, r is the interest rate as a decimal, and t is the time the money was borrowed.

Plug in the values and solve for t:

108 = (1200)(0.03)(t)

108 = 36t

3 = t

= 3 years

Answer:

720 different ways.

Step-by-step explanation:

Permutation has to do with arrangement. For example, in order to arrange 'n' objects in any order, this can only be done in n! ways since there is no condition or restriction on how to arrange the objects.

n! = n(n-1)(n-2)... (n-r)!

If there are 3 statistics books, 2 math books, and 1 computer science book on your bookshelf, the total number of books altogether is 3 + 2 + 1 = 6 books.

The number of ways that 6 books can be arranged in any order is 6!.

6! = 6(6-1)(6-2)(6-3)(6-4)(6-5)

6! = 6*5*4*3*2*1

6! = 120*6

6!= 720 different ways.

Hence, the books on your shelf can be arranged in 720 different ways.

Answer:

-2A = (-6, -8, 0, 8, 2, -8)

B - 2A = (2, -7, -4, 3, 4, -12)

AC is undefined.

CD = (3, 2, 12, 5)

Step-by-step explanation:

Given the matrices:

A = (3 4 0 -4 -1 4)

B = (8 1 -4 -5 2 -4)

C = (1 -1 3 1)

D = (3 -2 4 5)

We are required to compute the following

-2A, B - 2A, AC, CD

For -2A:

-2(3 4 0 -4 -1 4)

= (-6, -8, 0, 8, 2, -8)

For B - 2A:

Because B - 2A = B + (-2A), we have:

(8 1 -4 -5 2 -4) + (-6, -8, 0, 8, 2, -8)

(2, -7, -4, 3, 4, -12)

For AC:

(3 4 0 -4 -1 4)(1 -1 3 1)

This is undefined.

For CD:

(1 -1 3 1)(3 -2 4 5)

= (3, 2, 12, 5)

Answer:

210.33 cm^2

Step-by-step explanation:

We know that 6 equilateral triangles makes one hexagon.

Also, an equilateral triangle has all its sides equal.

If the tile of each side of the triangular tile measure 9 cm, then the height of the triangular tiles can be gotten using Pythagoras's Theorem.

The triangle formed by each tile can be split along its height, into two right angle triangles with base (adjacent) 4.5 cm and slant side (hypotenuse) of 9 cm. The height  (opposite) is calculated as,

From Pythagoras's theorem,

[tex]hyp^{2} = adj^{2} + opp^{2}[/tex]

substituting, we have

[tex]9^{2} = 4.5^{2} + opp^{2}[/tex]

81 = 20.25 + [tex]opp^{2}[/tex]

[tex]opp^{2}[/tex] = 81 - 20.25 = 60.75

opp = [tex]\sqrt{60.75}[/tex] = 7.79 cm  this is the height of the right angle triangle, and also the height of the equilateral triangular tiles.

The area of a triangle = [tex]\frac{1}{2} bh[/tex]

where b is the base = 9 cm

h is the height = 7.79 cm

substituting, we have

area = [tex]\frac{1}{2}[/tex] x 9 x 7.79 = 35.055 cm^2

Area of the hexagon that will be formed = 6 x area of the triangular tiles

==> 6 x 35.055 cm^2 = 210.33 cm^2

Answer:

1, 165.500

Step-by-step explanation:

1, 165.492 rounded to the nearest hundredth is 1, 165.500 because the hundredth space in the decimal is 5 or above, so the whole decimal gets rounded to the nearest hundred, which in this case, would be .500.

165.492 is the correct answer

Answer:

236°

Step-by-step explanation:

The circumference of a circle is 360° since <DOC is given as 44° and <COB is given as 80° and the center angles are equal to the arc it sees the the measure of arc DEB would be 360 - 44 - 80 = 236°

Answer:

259200

Step-by-step explanation:

so there are 86400 in one day. multiply by 3.

Answer:

259200

Step-by-step explanation:

60x24x3x60=

This is an arithmetic sequence because the difference

between the terms in the sequence remain constant.

In other words, we subtract 9 from one term to get the next.

So we start off with the explicit formula, shown below in yellow.

"n" will be the number of terms in the sequence,

a1 will be the first term in the sequence,

and d will be the common difference.

Now substitute these in like I have below.

You will get -425 as an answer.