Lydia has four straws of different lengths, and she is trying to form a right triangle. The lengths are 8, 9, 15, and 17 units. Which three lengths should she use? Justify your answer.

Using the arrangements formula, the probability of the butterscotch, cinnamon, and then chocolate candies eaten in this particular order is:

[tex]\frac{1}{6}[/tex].

The number of possible arrangements of n elements is given by the factorial of n, that is:

[tex]A_n = n![/tex]

In this problem, there are 3 candies, hence the number of ways they can be eaten is:

[tex]A_3 = 3! = 6[/tex]

The desired order is only one, hence the probability is:

[tex]\frac{1}{6}[/tex].

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Answer: 17 inches by 7 inches

Step-by-step explanation:

119 = 1 x 119 & 7 x 17

7 x 17 is the more likely answer, so let's test it

7 x 2 + 3 = 17

Therefore, the dimensions are 17 by 7.

The two figures are similar because each side length of the image is times the corresponding side length of the preimage and all the pairs of corresponding angles are congruent.

The transformations are given as:

Rotation and translation would preserve the lengths and the angles of the triangles. Because they are rigid transformations.

Dilation would only preserve the angle of the triangles. Because it is a nonrigid transformation.

The above means that the angles of triangle PQR and triangle P'Q'R' are congruent

Hence, the true statement is (d)

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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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The true statements are

The function g(x) is given as:

[tex]g(x) = -12(\frac 13)^x[/tex]

Set x = 0, to determine the y-intercept

[tex]g(0) = -12(\frac 13)^0[/tex]

g(0) = -12

From the table, we y-intercept of f(x) is

f(0) = -12

This means that they have the same y-intercept

Because the functions have negative initial values, they would approach negative infinity as x approaches negative infinity

Hence, the true statements are (d) and (e)

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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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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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The answer is 1

10¹ = 10

i hope it was helpful

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 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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Using it's concept, the standard deviation for the given data-set is of 8.22.

The mean for this problem is:

M = (17 + 26 + 28 + 9 + 30 + 29 + 6 + 21 + 23)/9 = 21

Hence the standard deviation is:

[tex]S = \sqrt{\frac{(17-21)^2 + (26-21)^2 + (28-21)^2 + \cdots + (21-21)^2 + (23-21)^2}{9}} = 8.22[/tex]

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Answer:

Step-by-step explanation:

A right triangle with one acute angle measuring 30° is the 30°-60°-90° "special" triangle. The ratios of its side lengths are well known to be ...

  1 : √3 : 2

In the given triangle, the longest side is labeled 10, so is 5 times the measure of the longest side in the ratios given above. Multiplying those ratio values by 5, we have side lengths ...

  a : b : c = 5 : 5√3 : 10

That is ...

  a = 5

  b = 5√3

__

Additional comment

If you want to figure the side lengths using trigonometry, you have ...

  a = c·sin(30°) = 10·(1/2) = 5

  b = c·cos(30°) = 10·(√3/2) = 5√3

Answer:

x = 15, UV = 12, SV = 31

Step-by-step explanation:

13 + 6 + (2x - 18) = 4x - 29

2x + 1 = 4x - 29

2x = 30

x = 15

UV = 2x - 18 = 2*15 - 18 = 30 - 18 = 12

SV = 4x - 29 = 4*15 - 29 = 60 - 29 = 31

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]

Answer:

19.50

Step-by-step explanation:

32m = 624

m = 19.50

need more words

The amount it costs to buy 88ft of crow molding is; $143.

It follows from the task content that the cost for 8ft length of a specific width crown molding is; $13.

On this note, it follows that the cost of buying 88ft of the same kind of crow molding can be estimated as;

88 × ($13/8)

= $143.

Therefore, the cost of 88ft of crow molding is; $143.

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[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:

d=27

Step-by-step explanation:

d+13=40

  -13  -13    Subtract 13 from both sides to leave by itself

d=27

Hope it helps:)

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

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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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

Answer:

A. True

Step-by-step explanation:

The ratio 1000 grams=1kilogram is correct.

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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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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Answer:

  -6

Step-by-step explanation:

A suitable calculator can find this for you directly.

-1 raised to an odd power is -1. That means an odd-index root of a negative number will be the opposite of the corresponding root of its absolute value:

  ∛(-216) = -∛216 = -6

__

Additional comment

Many calculators and spreadsheets do not respond well to requests for roots of negative numbers. A calculator with built-in support for complex numbers is the best choice for this sort of problem.

The second attachment shows a calculator capable of finding the complex roots as well as the real one.

The factors of 4x^2 +8x-5 are (2x-1) and (2x+5)

Answer:

18564 ways

Step-by-step explanation:

The number of committees is equal to the number of combinations of 6 members that we can form out of 18 person :

then

This can be done in [tex]C^{6}_{18}[/tex]  ways.

[tex]C^{6}_{18}=\frac{18!}{6!\left(18-6 \right)! } = 18564[/tex]

The given numbers written in standard forms are

1.0 × 10⁷

1.0 × 10⁵

1.0 × 10⁸

1.0 × 10¹²

1.0 × 10⁶

respectively

From the question, we are to write the given numbers in standard form

To write the given numbers in standard form,

Multiply each of the numbers by 1.0

Then,

10⁷ in standard form is 1.0 × 10⁷

10⁵ in standard form is 1.0 × 10⁵

10⁸ in standard form is 1.0 × 10⁸

10¹² in standard form is 1.0 × 10¹²

10⁶ in standard form is 1.0 × 10⁶

Hence, the given numbers written in standard forms are

1.0 × 10⁷

1.0 × 10⁵

1.0 × 10⁸

1.0 × 10¹²

1.0 × 10⁶

respectively

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