A piece of wood is 5 m long. It is cut into pieces. The lengths of the pieces are in the ratio 4:3:2:1. The longest piece is then cut in the ratio 4:1 so that there are now five pieces. How long is the smallest piece?​

The length of ladder is 30 ft.

The formula below can be used in solving the problem

Tan (∅)= [tex]\frac{opposite}{adajacent}[/tex]

∅=70°

opposite = BC

Adjacent  = 12 ft

70°= opposite/ 12

opposite= 32.96 ft

Therefore, The length of ladder is 30 ft.

NOTE; Since the actual diagram can not be found i solved another on on the same topic

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CHECK COMPLETE QUESTION BELOW:

Consider the diagram shown where a ladder is leaning against the side of a building. the base of the ladder is 12ft from the building. how long is the ladder? (to the nearest ft)

a. 25ft

b. 30ft

c. 35ft

d. 40ft

The value of the modulus function |-3| is 3.

'Modulus' exists a Latin word, which signifies 'measure'. Absolute value is commonly referred to as numeric value or magnitude. The absolute value designates only the numeric value and does not contain the sign of the numeric value. The modulus of any vector quantity exists ever taken as positive and exists in its absolute value.

The absolute value (or modulus) | x | of a real number x stands as the non-negative value of x without regard to its sign.

For example, the absolute value of 5 stands at 5, and the absolute value of −5 exists also at 5. The absolute value of a number may be considered as its distance from zero along a real number line.

Therefore, the value of the modulus function |-3| is 3.

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See below for the examples of sectors and arcs of a circle

The area of a sector is calculated as:

[tex]A = \frac{\theta}{360} * \pi r^2[/tex] ---- when the angle is in degrees

[tex]A = \frac{\theta}{2} *r^2[/tex] ---- when the angle is in radians

Take for instance, we have the following problems involving sector areas

Calculate the area of a sector where the radius of the circle is 7, and

Using the above formulas, the sector areas are:

1. [tex]A = \frac{30}{360}* \frac{22}{7} * 7^2 = 12.83[/tex]

2.  [tex]A = \frac{\pi}{12} * 7^2 = 12.83[/tex]

3. [tex]A = \frac{90}{360}* \frac{22}{7} * 7^2 = 38.5[/tex]

4. [tex]A = \frac{\pi}{2} * 7^2 = 38.5[/tex]

5. [tex]A = \frac{180}{360}* \frac{22}{7} * 7^2 = 77[/tex]

The length of an arc is calculated as:

[tex]L= \frac{\theta}{360} * 2\pi r[/tex] ---- when the angle is in degrees

[tex]L = r\theta[/tex] ---- when the angle is in radians

Take for instance, we have the following problems involving arc lengths

Calculate the length of an arc where the radius of the circle is 7, and

Using the above formulas, the arc lengths are:

1. [tex]L = \frac{30}{360}* 2 * \frac{22}{7} * 7 = 3.7[/tex]

2.  [tex]L = \frac{\pi}{12} * 7 = 3.7[/tex]

3. [tex]L = \frac{90}{360}*2 * \frac{22}{7} * 7 = 11.0[/tex]

4. [tex]L = \frac{\pi}{4} * 7 = 11[/tex]

5. [tex]L = \frac{180}{360}*2 * \frac{22}{7} * 7 = 22[/tex]

The examples include:

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a. The reason why this question is a binomial experiment is based on the fact that it is made up of an independent sample, it has a number that is fixed and a probability.

Each event is made up of two outcomes and they are random with the same success rate.

we have the following data n = 12, p = 0.27 and k = 5

We have to use the function to solve electronically

binompdf(n,p,k)

input the values

= binompdf(12,0.27,5)

This gives us

= 0.1255

We use the formula below

= binompdf(12,0.27,5-1)

This is = 0.7984

D. Probability of at least 5

1 - probability of fewer than 5

= 1 - 0.7984

= 0.2016

How to solve for the Mean = n*p

n = 12 , p = 0.27

Mean = 12*0.27 = 3.24

and

standard deviation = √npq

n = 12, p = 0.27 , q = 1- 0.27

= 0.73

sd = √12*.27*.73

= 1.54

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Multiplication of 3495 by 30595 is: 106,929,525.

Multiplication can be defined as the way of multiplying a number by another name.

Using  a calculator to multiply  3495 by 30595.

Hence:

Multiplication= 3495×30595

Multiplication= 106,929,525

Therefore Multiplication of 3495 by 30595 is: 106,929,525.

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The proofing for the triangle is illustrated below.

The proofing for a² + b² = c² in the triangle is illustrated.

It should be noted that the longest side in the triangle is the hypothenuse. The hypothenuse is gotten by finding the square root of the opposite and the adjacent.

Therefore, a² + b² = c²

Let's say a = 3 and b = 4, the value of c will be:

c² = a² + b²

c² = 3² + 4²

c² = 9 + 16

c² = 25

c = ✓25

c = 5

Also, the square and triangle is illustrated and attached.

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The true statement is that Alex is 50% taller than Dan.

They both measured themselves against a tree in their backyard.

Therefore, the tree is 80% taller than Dan and 20% taller than Alex.

Hence,

let

Dan height = x

Tree's height = x + 0.8x

Tree's height = 1.8x

let

Alex height = y

Tree's height = y + 0.2y

Tree's height = 1.2y

Therefore, if we use Dan height as 100, the height of the tree will be 180.

Then,

180 = 1.2y

y = 150

This means Alex is 50 percent taller than Dan.

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The exponential form of 6 × 6, is written as: 6².

Repeated multiplication involving base exponents and base can be written in exponential form, such as: a × a × a = a³.

Given the expression, 6 × 6, the number 6 will be the base while 2 will be the exponent if we want to express it in exponential form. Therefore:

6 × 6 = 6².

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The annual interest rate needed to reach the given amount in five years is 4.47%.

Hence, option B) is the correct answer.

Compound interest is expressed as;

A = P( 1 + r/n )^(nt)

Making rate r the subject of the formula;

r = n[ (A/P)^(1/nt) - 1 ]

Given that;

We substitute into our formular above

r = n[ (A/P)^(1/nt) - 1 ]

r = 12[ (2500/2000)^(1/(12×5)) - 1 ]

r = 12[ (1.25^(1/60) ) - 1 ]

r = 12[ 1.0037598 - 1 ]

r = 12[ 0.0037598 ]

r = 0.447

Next we convert to percentage

r = 0.447 × 100%

r = 4.47%

The annual interest rate needed to reach the given amount in five years is 4.47%.

Hence, option B) is the correct answer.

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Answer:

240 pages

Step-by-step explanation:

Let x = the TOTAL number of pages in the book. So we'll add up all her reading for the week and it should equal x, the total number of pages.

see image.

The simplified firm of the ratio 0.40 to 0.60 is 2 : 3

0.40 : 0.60

= 0.40 / 0.60

divide both numerator and denominator by 0.20

= 2 / 3

= 2 : 3

Therefore, the simplified form of the ratio 0.40 to 0.60 is 2 : 3

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Solving a system of equations we will see that they sold 80 adult tickets.

To solve this, we need to solve a system of equations. To define said systems of equations, we first need to define the variables, we will use:

They sold 20 more adult tickets than student tickets, then:

x = y + 20

And they collected a total of $880, then:

x*$8 + y*$4 = $880

The the system of equations is:

x = y + 20

x*$8 + y*$4 = $880

Isolating y on the first equation we get:

y = x - 20

Replacing that on the other equation we get:

x*$8 + (x - 20)*$4 = $880

Now let's solve that for x.

x*$12 - $80 = $880

x*$12 = $880 + $80 = $960

x = $960/$12 = 80

They sold 80 adult tickets.

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The final percent of juice is 10%

We initially have one quart that is 40% juice and 60% water.

Then initially we have:

Then we add another 3 quarts of water, so the new mixture has:

So we have 4 quarts of mixture.

The new percentage of juice will be:

P = (0.4 quarts/4 quarts)*100% = 10%

The final percent of juice is 10%

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Answer:

A

Step-by-step explanation:

It is the quadratic parent function

The missing values of the right angle triangle are; a = 28 yds; c = 47 yds; ∠B = 54°

From the attached image of the right angle ABC, we see that;

∠A = 36°

b = 38 yd

∠C = 90°

Using trigonometric ratios, we have;

a/38 = tan 36

a = 38 * tan 36

a = 27.61 yd ≈ 28 yds

Similarly;

38/c = cos 36

c = 38/cos 36

c = 46.97 yds ≈ 47 yds

∠B = 180 - (36 + 90)

∠B = 54°

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The value of the ratio based on the angle illustrated is 1:12.

From the information given, it should be noted that the angle in a circle is 360°. Therefore, the value of theta will be:

= 360° - 330°

= 30°

The equivalent expression based on the angle will be:

= 30/360

= 1/12

= 1:12

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Answer:   About the building of his bed

The equivalent to the quotient shown in the task content for acceptable values of x is; √(5/(x-1)).

It follows from the task content that the expression given is; √(25(x-1)) ÷ √(5(x-1)²).

It therefore follows from the the laws of indices that the evaluation is thus;

= √{(25/5) ×(x-1)/(x-1)²}.

Ultimately, upon evaluation we have;

= √(5/(x-1))

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Answer:

60 cubic inches

Step-by-step explanation:

You multiply 3 and 4 to get 12, then 12 and 5 to get 60

3 x 4 x 5 = 60

The volume of a solid exists the measurement of how much area an object brings up. It exists measured by the number of unit cubes it brings to fill up the solid.

Volume of a solid = 5 [tex]*[/tex] 3 [tex]*[/tex] 4 = 60 cubic inches

Therefore, the correct answer is option d) 60 cubic inches.

Volume exists as a three-dimensional measurement; that exists, it measures the collective length, width, and height of a figure. Because planes, polygons, and other two-dimensional figures don't contain height, they contain no volume. Only solids and figures with dimensions more significant than or equivalent to three have volume.

The volume of a solid exists as the measurement of how much space an object brings up. It exists estimated by the number of unit cubes it brings to fill up the solid.

Volume of a solid = 5 [tex]*[/tex] 3 [tex]*[/tex] 4 = 60 cubic inches

Therefore, the correct answer is option d) 60 cubic inches.

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Answer:

1.The slope intercept- form of the function is:

y = x -2

2.The predicted length of the vine after 53 days is 51 cm.

Step-by-step explanation:

The slope is the [tex]\frac{change in length}{change in days}[/tex]  

In the table, every time that the length increased by 5, the days also increased by 5.  5/5 = 1

Now we have to find the y-intercept, we can use the slope and one of the points that we know to do this.  Let's use the first point (5,3). This is in the form (x,y).

y = mx + b

3 = (1)(5) + b

3 = 5 + b   Subtract both sides by 5

-2 = b  Now we can write the equation

y = mx + b

y = x -2.  Plug 53 in for x and you will find your second answer.

y = 53 - 2

y = 51

1. The function's slope intercept form is y = x -2.

2. The vine should be 51 cm long in length after 53 days.

Determining the Slope Intercept Form:

The slope is given as,

m = (Change in length) / (Change in days)

In the table, it can be seen that,

The days climbed by 5 for every 5 that the length did as well [10-5 = 8-3 = 5].

∴ Slope, m =5/5 = 1

We may use the slope and one of the points we are familiar with to help us find the y-intercept. Utilizing the first point (5,3), this is how it looks for the point (x, y),

y = mx + c ..... (1)

3 = (1)(5) + c

3 = 5 + c

Subtract 5 from both sides to get c.

c = -2

Hence, from (1), the slope intercept form is given as,

y = x - 2 ...... (2)

Predicting the Vine Length:

Since x represents the number of days, put x = 53 in equation (2) to predict the vine length after 53 days.

y = (53) -2

y = 51 cm

Thus, the length of vine after 53 days would be 51 cm.

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Work Shown:

(arc YZ + arc XU)/2 = angle YVZ

(arc YZ + 38)/2 = 90

arc YZ + 38 = 90*2

arc YZ + 38 = 180

arc YZ = 180 - 38

arc YZ = 142

[tex]r = 3sec( \alpha ) \\ r = \frac{3}{cos( \alpha )} [/tex]

[tex]x = rcos( \alpha ) \: \: \: \: \: \: \: cos( \alpha ) = \frac{x}{r} [/tex]

[tex]r = \frac{3}{ \frac{x}{r} } \\ r = \frac{3r}{x} \: \: \: \: \: \: x = 3 \\ line[/tex]

Answer:

10.4403 or the square root of 109

Step-by-step explanation:

We do this by finding the height (3) and squaring it then the base (10) and squaring that, this sets up the Pythagorean theorem which is A^2+B^2=C^2 then you square C to find it's value

Answer: [tex]\cos^{-1} \left(\frac{-22}{\sqrt{754}} \right)[/tex]

Step-by-step explanation:

[tex]a \cdot b=(3)(0)+(-4)(5)+(-1)(2)=-22\\\\|a| |b|=\sqrt{3^2 +4^2 +1^2} \sqrt{5^2 +2^2}=\sqrt{754}\\\\\therefore \cos \theta=\frac{-22}[\sqrt{754}}\\\\\theta=\cos^{-1} \left(\frac{-22}{\sqrt{754}} \right)[/tex]

The simple interest rate that the money would be paid is 20%

From the question, we are to determine the interest rate that the money would be paid

Using the formula for simple interest,

S.I = PRT/100

Where S.I is the simple interest

P is the principal

R is the rate

and T is the time

From the given information,

P = 2000

S.I = Amount - Principal = 3600 - 2000 = 1600

R = ?

T = 4

Putting the parameters into the equation, we get

1600 = (2000 ×R × 4) / 100

1600 = 20 × R × 4

1600 = 80R

R = 20%

Hence, the simple interest rate that the money would be paid is 20%

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Answer:

22.6

Step-by-step explanation:

a^2+b^2=c^2

8^2+b^2=24^2

b^2=512

b=22.6

Answer:

[tex]x = 16\sqrt{2}[/tex]

Step-by-step explanation:

we are given a right triangle.

then

In order to determine x we need to use

the Pythagorean theorem:

[tex]x^{2}+8^{2}=24^{2}[/tex]

⇔ x² + 64 = 576

⇔ x² = 576 - 64

⇔ x² = 512

⇔ x² = 2⁹

⇔ x² = 2 × 2⁸

[tex]\Longleftrightarrow x=\sqrt{2\times 2^{8}} =\sqrt{2\times \left( 2^{4}\right)^{2} }[/tex]

[tex]\Longleftrightarrow x= \sqrt{\left( 16\right)^{2} } \times \sqrt{2[/tex]

[tex]\Longleftrightarrow x = 16\sqrt{2}[/tex]

The value of the probability is 0.54

The given parameters are:

P(A) = 0.35

P(B) = 0.54

From the question, we understand that the events are independent.

This means that

P(B|A) = P(B)

Substitute P(B) = 0.54

P(B|A) = 0.54

Hence, the value of the probability is 0.54

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