18. In AABC, 44 is a right angle, and m4B 45°. What is the length of BC? If the answer is not an integer, leave it in simplest radical form. The
diagram is not drawn to scale.

054 ft

17√3 ft

17√2 ft

017

Reduce the numbers in the list modulo 3 to get the set

{1, 2, 0, 1, 2, 0, …, 1, 2, 0}

containing [tex]k[/tex] copies each of 1, 2, and 0.

Take any 3 elements from the list. Their sum is divisible by 3 if those elements' residues also sum to 3 ≡ 0 (mod 3). To get a sum of 0, we must make one of the following choices:

0 + 0 + 0 ≡ 0 (mod 3)

1 + 1 + 1 ≡ 3 ≡ 0 (mod 3)

2 + 2 + 2 ≡ 6 ≡ 0 (mod 3)

0 + 1 + 2 ≡ 3 ≡ 0 (mod 3)

There are

[tex]\dbinom k3 \dbinom k0 \dbinom k0 = \dfrac{k(k-1)(k-2)}6[/tex]

ways of choosing 3 elements with a given residue and 0 elements with any other residue, hence

[tex]3\dbinom k3\dbinom k0\dbinom k0 = \dfrac{k(k-1)(k-2)}2[/tex]

ways of choosing any 3 elements with the same residue, and there are

[tex]\dbinom k1 \dbinom k1 \dbinom k1 = k^3[/tex]

ways of choosing any 3 elements with distinct residues.

So, the total number of ways of making the selection is

[tex]3\dbinom k3\dbinom k0^2 + \dbinom k1^3 = \boxed{\dfrac32 k^3 - \dfrac32 k^2 - k}[/tex]

Answer:

(-2, 2)

Step-by-step explanation:

Given system of equations:

[tex]\begin{cases}y=x+4\\y=-2x-2 \end{cases}[/tex]

To solve by substitution, substitute the first equation into the second equation:

[tex]\implies x+4=-2x-2[/tex]

Add 2x to both sides:

[tex]\implies x+4+2x=-2x-2+2x[/tex]

[tex]\implies 3x+4=-2[/tex]

Subtract 4 from both sides:

[tex]\implies 3x+4-4=-2-4[/tex]

[tex]\implies 3x=-6[/tex]

Divide both sides by 3:

[tex]\implies \dfrac{3x}{3}=\dfrac{-6}{3}[/tex]

[tex]\implies x=-2[/tex]

Substitute the found value of x into the first equation and solve for y:

[tex]\implies y=-2+4[/tex]

[tex]\implies y=2[/tex]

Therefore, the solution to the given system of equations is (-2, 2).

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Substitute y value from first eqn in second equation

Put in first one

(-2,2) is the solution

Answer: (0, 16)

Step-by-step explanation:

y = mx + c

c is the y intercept

from the equation, c = 16

(it's not exactly mx but you don't need to solve for x)

The length of the square pool is 8. 49cm

Note that the formula for finding the area of a square is given as;

Area = length^2

We have

Area = 72 m²

Substitute into the formula

I^2 = 72

Find the square root of both sides

I= √72

I = 8. 49cm

The length of the square pool given as I is 8. 49cm

Thus, the length of the square pool is 8. 49cm

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Answer:

x = 30

Step-by-step explanation:

110 and 3x - 20 are supplementary angles, sum to 180° , then

110 + 3x - 20 = 180

90 + 3x = 180 ( subtract 90 from both sides )

3x = 90 ( divide both sides by 3 )

x = 30

Answer:

x = 30

Step-by-step explanation:

Please refer to the attached photo. (Apologies for the terrible drawing.)

For this question, you must be clear of the angle properties.

z + 110 = 180 (Sum of Angles on a straight line)

z = 180 - 110 = 70

z = 3x - 20 (Corresponding Angles)

3x - 20 = z

3x - 20 = 70

3x = 70 + 20

3x = 90

x = 90 / 3 = 30

Answer:

7 - 10

Step-by-step explanation:

Because it is -3 and 7 - 10 = -3

Answer: 6 bees

Step-by-step explanation:

The picture has 12 bees and 10 flowers. Thus, the ratio of flowers to bees is 10 to 12, which simplifies to 5 to 6.

Therefore, for every 5 flowers, there are 6 bees.

The equivalent form of the equation y=[tex]x^{2} -2x-15[/tex]given is y=(x+3)(x-5).

Given an equation y=[tex]x^{2}[/tex]-2x-15 and we are required to find the equivalent form of the equation.

Equation is like a relationship between two or more variables that are expressed in equal to form. Equation of two variables look like ax+by=c. It may be linear equation, quadratic equation, cubic equation or any other equation  depending on the powers of the variable.

To find the equivalent equations we are required to form factors of the equation. Equivalent equation are those equations which when solved gives the same solution as the equation when solved gives.

y=[tex]x^{2}[/tex]-2x-15

y=[tex]x^{2}[/tex]-5x+3x-15

y=x(x-5)+3(x-5)

y=(x+3)(x-5)

Hence the equivalent form of the equation y= [tex]x^{2}[/tex]-2x-15 given is

y=(x+3)(x-5).

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Question is incomplete as question should includes the equation

y= [tex]x^{2}[/tex]-2x-15.

The value of the Mean & Standard deviation is 1.30 and 1.18.

According to the statement

we have a given that the random variable x represents the number of computers that families have along with the corresponding probabilities.

And we have to find the mean and standard deviation from the given data which is related to the probabilities values

So, according to the given data

The formula to compute the mean is:

Mean = summation [x*p(x)]

Compute the mean as follows:

Mean = summation [x*p(x)]

Mean = summation [0*0.49 + 1* 0.05 + 2*0.32 + 3*0.07 + 4*0.07]

Mean = 0 +0.05 + 0.64 + 0.21 + 0.28

Mean = 1.18

The mean of the random variable x is 1.18.

And after calculating the variance from the formula get

The value of standard deviation is 1.30

So, The value of the Mean & Standard deviation is 1.30 and 1.18.

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Answer:

5x - y = 9

Step-by-step explanation:

the equation of a line in standard form is

Ax + By = C ( A is a positive integer and B, C are integers )

given

y = 5x - 9 ( subtract 5x from both sides )

- 5x + y = - 9 ( multiply through by - 1 )

5x - y = 9 ← in standard form

Answer:

8

Step-by-step explanation:

because hhhhhh

gghhhh

jkkkkk

lllll

vvvvv

dddfff

oooooo

eeeerer

kkkkkk

lllll.ssss

On purchasing a cell phone, Tia got an offer and got the cell phone for 35% less than the tag price. If she saved 140 on that cell phone. Then price on the tag is 400.

Since, the cell pone is sold with 35% discount on it.

Tia got that phone at selling price with 35% discount on tag price. Also, she saved around 140 on buying the cell phone.

Therefore, the discount on the cell phone on the tag price is her saving on buying the cell phone.

Hence,

35% discount on tag price=Saved amount

(35/100)×T=140

where T is the tag price.

T=(140×100)35

T=14000/34

T=400

Therefore, on buying the cell phone with 35% discount on tag price costs around 140. Then the tag price is 400.

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Answer: 9 triangles.

Step-by-step explanation:

Just make a dot in the middle and make lines and connect each line to an edge or bend.

The measure of the angle of depression from the helicopter to the girl’s line of sight is 67 degrees.

A right angle triangle has one of its angle as 90 degrees. The sides and angles can be found using trigonometric ratios.

Therefore, angle of depression from the helicopter can be found as follows:

tan x = opposite / adjacent

where

x = angle of depression

Hence,

tan x = 660 / 280

tan x = 2.35714285714

x = tan⁻¹ 2.35714285714

x = 67.1231281953

x = 67°

Therefore, the measure of the angle of depression from the helicopter to the girl’s line of sight is 67 degrees.

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Answer:

D = 67

Step-by-step explanation:

The weight that separates the top 4% is x = 7.87 (round nearest hundredth) .

The weight that separates the bottom 4% is x = 7.63 (round nearest hundredth).

The majority of the observations are centred around the middle peak of the normal distribution, which is a continuous distribution of probability that really is symmetrical around in its mean.

The probability for values that are farther from of the mean tapered down equally both in directions.

Now, use z-chart to find the z-value for that separates the top 4% and the bottom 4%.

The values of z = +1.75 and z = -1.75

Let the weight of the machines be 'x'.

Use the formula for z- value

z = (x -  μ)/ σ

Where,

σ  is standard deviation =  0.07 ounces.

μ is mean = 7.75 ounces.

Substitute all the values and calculate the weight.

case 1: when z = +1.75

1.75 = (x - 7.75)/0.07

x  = (1.75×0.07) + 7.75

x = 7.872

x = 7.87 (round nearest hundredth)

case 2: when z = -1.75

-1.75 = (x - 7.75)/0.07

x  = (-1.75×0.07) + 7.75

x = 7.6275

x = 7.63 (round nearest hundredth)

Therefore,

x = 7.87 (round nearest hundredth) is weight which separates top 4%.

x = 7.63 (round nearest hundredth) is weight which separates bottom 4%.

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Hello,

x² + 5x + 6 = 0

a = 1 ; b = 5 ; c = 6

∆ = b² - 4ac = 5² - 4 × 1 × 6 = 25 - 24 = 1 > 0

2 solutions :

[tex] x_{1} = \frac{ - b - \sqrt{\Delta} }{2a} = \frac{ - 5 - 1}{2 \times 1} = \frac{ - 6}{2} = - 3[/tex]

[tex]x_{2} = \frac{ - b + \sqrt{\Delta} }{2a} = \frac{ - 5 + 1}{2 \times 1} = \frac{ - 4}{2} = - 2[/tex]

S = { -3 ; -2}

Answer:

6.80 x 10⁻⁷ m

Step-by-step explanation:

You can find the value of λ by inserting the given values into the equation and simplifying.

c = vλ                                                            <----- Given equation

2.998 x 10⁸ m/s = (4.41 x 10¹⁴ s⁻¹)λ               <----- Insert values

6.80 x 10⁻⁷ m = λ                                          <----- Divide both sides by 4.41 x 10¹⁴

1a) f(x) = -1/3(x + 12)² + 9

1b) f(x) = -1/3x² - 8x - 39

Lets simplify it,

Expand by FOIL (First Outside Inside Last)

Standard Form: ax² + bx + c = 0

Transformations Graph: f(x) = a(bx - c)² + d

Reflected down and vertically stretched by 1/3:   a = -1/3

Shifted vertically by 9 units:   d = 9

Shifted horizontally by -12 units:   c = -12

Vertex Form:

 f(x) = a(bx - c)² + d

 f(x) = -1/3(x + 12)² + 9

Standard Form:

f(x) = -1/3(x + 12)² + 9

f(x) = -1/3(x² + 24x + 144) + 9

f(x) = -1/3x² - 8x - 48 + 9

f(x) = -1/3x² - 8x - 39

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Answer: 30 degrees

Step-by-step explanation:

The total number of ties present in the bag are 130.

Calculating or estimating how likely something is to occur is what probability is all about. The likelihood of an event occurring can be expressed using words like "certain," "impossible," or "probable."

Formula for probability is -

Probability(Event) = Favourable Outcomes/Total Outcomes

It P(E) is the probability for occurring any event.

'x' be the favourable outcome.

'n' be the total outcome.

Then,

P(E) = x/n.

Calculation for the total tiles present the bag.

The probability of choosing a vowel is 40% = 0.4.

Then, the probability of choosing a consonants will be 1 - 0.4 = 0.6 or 60%.

Let P(E) be the probability of the occurrence of the consonants.

Then,

P(E) = total number of consonants/total tiles in the bag.

Let 'T' be the total tiles in the bag.

0.6 = 78/T

T = 78/0.6

T = 130

Therefore, the total tiles present in the bag are 130.

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Answer:

22 millilitres of 13% solution

23 millilitres of 19% solution

Step-by-step explanation:

A + B = 45

13A + 19B = 45 x 17 = 765

-13A - 13B + 13A + 19B = -650 + 765 = 115

5B = 115

B = 23

22 + 23 = 45

A = 22

Answer: 3

Step-by-step explanation:

Multiply the numerator to get 3 x 6 is 18

Multiply the denominator to get √6 x √6 = 6

Divide 18 by 6 to get the answer is 3

The equation that represents the relationship between n and w is w = 10n + 8.

From the information, Ron is making a banner by stringing letters on a cord and the cord weighs 8

ounces and each letter weighs 10 ounces.

Let represent the number of letters

Let w represent the weight of the banner.

In this case, when n = 6, w = 68 and when n = 7, w = 78.

Therefore, the relationship will be:

w = 10n + 8

To confirm let's use n = 6

10n + 8

10(6) + 8

= 68

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Answer:

Step-by-step explanation:

w=10n+8

Amie's error while measuring the volume of a sphere is that Amie should have multiplied 54 by 2/3. Thus, the first option is the right choice.

In the question, we are given that a sphere and a cylinder have the same radius and height.

We assume the radius of the sphere to be r, and its height to be h.

Now, the height of a sphere is its diameter, which is twice the radius.

Thus, the height of the sphere, h = 2r

Given that the sphere and the cylinder have the same radius and height, the radius of the cylinder is r, and its height is 2r.

The volume of a sphere is given by the formula, V = (4/3)πr³, where V is its volume, and r is its radius.

Thus, the volume of the given sphere using the formula is (4/3)πr³.

The volume of a cylinder is given by the formula, V = πr²h, where V is its volume, r is its radius, and h is its height.

Thus, the volume of the given cylinder using the formula is πr²(2r) = 2πr³.

Now, to compare the two volumes we take their ratios, as

Volume of the sphere/Volume of the cylinder

= {(4/3)πr³}/{2πr³}

= 2/3.

Thus, the volume of the sphere/the volume of the cylinder = 2/3,

or, the volume of the sphere = (2/3)*the volume of the cylinder.

Given the volume of the cylinder to be 54 m³, Amie should have multiplied 54 by 2/3 instead of adding the two.

Thus, Amie's error while measuring the volume of a sphere is that Amie should have multiplied 54 by 2/3. Thus, the first option is the right choice.

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For the complete question, refer to the attachment.

Answer:

Below in bold.

Step-by-step explanation:

That would be 4/15 * 360   as there are 360 degrees in a circle

= 96 degrees.

The value of 2+8+32+128…..,n=9 is 174762

The series is given as:

2+8+32+128…..,n=9

Start by calculating the common ratio (r)

r = 8/2

r = 4

The sum of the series is then calculated as:

[tex]S_n = \frac{a *(r^n - 1)}{r -1}[/tex]

This gives

[tex]S_9 = \frac{2 *(4^9 - 1)}{4 -1}[/tex]

Evaluate the difference

[tex]S_9 = \frac{2 *( 262143)}{3}[/tex]

Evaluate the quotient

[tex]S_9 = 174762[/tex]

Hence, the value of 2+8+32+128…..,n=9 is 174762

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Answer:

a.) An open circle on 4 with a solid line drawn to an open circle on -4.

Explanation:

Open circles are used for signs: < and >

Closed circles are used for signs: ≤ and ≥

Here in the given expression: |x| < 4

[<] sign is used so open circle is used

If |y| < a then -a < y < a

so here, -4 < x < 4

Both circles should be opened, drawn with a solid line from -4 to 4.

Answer:

8:35 PM

Step-by-step explanation:

First, subtract 15 from 50.

50-15=35

Add that 15 taken from 50 to 7:45.

7:45 + 0:15 = 8:00

Add 35 to 8:00

8:00 + 0:35 = 8:35

The next movie will start at 8:35 PM.

Hope this helps!

Step-by-step explanation:

Answer:

a= 100.2

Step-by-step explanation:

You solve it like you ate looking for the hypotenuse