Find the value of x on this triangle

Answer:

[tex]x =320[/tex]

Step-by-step explanation:

Given

[tex]x^2 + 200x = 166400[/tex]

Required

Find x

We have:

[tex]x^2 + 200x = 166400[/tex]

Rewrite as:

[tex]x^2 + 200x - 166400 = 0[/tex]

Expand

[tex]x^2 + 520x - 320x - 166400 = 0[/tex]

Factorize

[tex]x(x + 520) - 320(x + 520)= 0[/tex]

Factor out x + 520

[tex](x - 320) (x + 520)= 0[/tex]

Split

[tex]x - 320 = 0\ or\ x + 520= 0[/tex]

Solve

[tex]x = 320\ or\ x =- 520[/tex]

Side length must be positive;

So:

[tex]x = 320[/tex]

Answer:

Square Root of 529:√529 = 23

Square Root of 1080: 32.863353450309965

Answer:

The drone takes 2.25 seconds to be higher than the basketball.

Step-by-step explanation:

Based on the definitions given on statement and the image attached below, the red line represents the height of the basketball and the blue line represents the height of the drone, respectively. The height of the drone is higher than the height of the basketball when the y-value of the former is higher than the y-value of the latter. The time is contained in the +x semiaxis.

According to the figure, the drone takes 2.25 seconds to be higher than the basketball.

Answer:

The probability of both dice having the same number is 636, as there are 36 different outcomes, 6 of which have two of the same number, i.e. (1,1),(2,2),....

The expected number of rolls of this type in 100 pairs of dice rolls is 100∗636

Answer:

4:16 = 0.25

Step-by-step explanation:

16 outcomes are possible, 4 with the same number.

Complete question is;

Engineers are designing a large elevator that will accommodate 58 people. The maximum weight the elevator can hold safely is 11,716 pounds. According to the National Health Statistics Reports, the weights of adult U.S. men have mean 190 pounds and standard deviation 62 pounds, and the weights of adult U.S. women have mean 184 pounds and standard deviation 71 pounds. Use the TI-84 Plus calculator.

Required:

a. If 58 people are on the elevator, and their total weight is 11,716 pounds, what is their average weight?

b. If a random sample of 58 adult men ride the elevator, what is the probability that the maximum safe weight will be exceeded?

Answer:

A) average weight = 202 pounds

B) the probability that the maximum safe weight will be exceeded = 42.47%

Step-by-step explanation:

A) We are told that 58 people are on the elevator and that their total weight is 11,716 pounds. Thus;

Average weight = total weight/number of people = 11716/58 = 202 pounds

B) We will use z-score formula in this;

z = (x¯ - μ)/σ

Now, in part a above, we saw that the average weight is 202 pounds. Thus; x¯ = 202 pounds

We are told that standard deviation for men is;

σ = 62 pounds

We are told that the weights of adult U.S. men have mean 190 pounds . Thus; μ = 190

Thus;

z = (202 - 190)/62

z = 0.19

From z-distribution table, p-value = 0.57535

Thus;

P(z > 0.19) = 1 - 0.57535 = 0.42465

Thus, the probability that the maximum safe weight will be exceeded = 0.42465 ≈ 42.47%

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Answer:

  3 ⇒ 12

Step-by-step explanation:

Apparently "a = b" in this case is used to mean f(a) = b. It appears as though the function is ...

  f(x) = x(x+1)

Then f(3) = 3(3+1) = 3·4 = 12

_____

Additional comment

IMO this is a poor use of the equal sign, which should be reserved for situations where the left side expression has the same value as the right side expression.

Answer:

n+3

Step-by-step explanation:

1/2 × 2(n+3)=n +3

I hope this helps

Answer:

tk 30

Step-by-step explanation:

5 dozen = 5 * 12 = 60 oranges

12/4 = 3

total cost = 60 * 3 = tk.180

total sell = 50 * 3 = tk 150

total lose = 180 - 150 = tk 30

Answer:

x² - √3x / x² - 3

Step-by-step explanation:

To Do :-

Solution :-

We need to rationalize ,

Multiply numerator and denominator by x-√3 :-

9514 1404 393

Answer:

Step-by-step explanation:

The perimeter ratio smaller : larger is the same as the side length ratio.

  18 : 24 = 3 : 4 . . . smaller : larger perimeter ratio

The area ratio is the square of this.

  3^2 : 4^2 = 9 : 16 . . . smaller : larger area ratio

Answer:

Null hypothesis :

H0 : Quality of parts produced been independent of the production process

We will reject Null hypothesis if value of test statistic ( x^2) > critical value of x^2 at significance level ( ∝ ) 0.05

Step-by-step explanation:

Part produced = QV2Y

Part can be produced using three ( 3 ) different production process

Production process results

process 1 : 29 defective in  240

significance level = 0.05

Null hypothesis :

H0 : Quality of parts produced been independent of the production process

We will reject Null hypothesis if value of test statistic ( x^2) > critical value of x^2 at significance level ( ∝ ) 0.05

critical value = 5.99147   where df = 2

answer: 77

Step-by-step explanation:

7×11=77

sorry if I'm wrong

Answer:

fijatebie nl aperguntaa

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

Shape = Isosceles Trapezoid

Area = 1/2 (a+b) h

= 1/2 (9+3) x 3

= 18

Answered by Gauthmath

Answer:

Step-by-step explanation:

Probability(P) (k events out of n trials) = nCk * p^k * (1-p)^(n-k), where p=0.40, n=10 and nCk is the number of combinations of n things taken k at a time

:

P ( k < or = 3 ) = P ( k = 3 ) + P ( k = 2 ) + P ( k = 1 ) + P ( k = 0 )

:

P ( k = 3 ) = 10C3 * (0.40)^3 * (0.60)^(10-3) = 0.2149

:

P ( k = 2 ) = 10C2 * (0.40)^2 * (0.60)^(10-2) = 0.1209  

:

P ( k = 1 ) = 10C1 * (0.40)^1 * (0.60)^(10-1) = 0.0403

:

P ( k = 0 ) = 10C0 * (0.40)^0 * (0.60)^(10-0) = 0.0060

:

******************************************************************************

P ( k < or = 3 ) = 0.2149 + 0.1209 + 0.0403 + 0.0060 = 0.3821 is approximately 0.38

The probability that when 14 adults are randomly selected and 3 or fewer are in excellent health is 0.072

Probability shows possibility to happen an event, it defines that an event will occur or not. The probability varies from 0 to 1.

Given that,

The percentage of adults who reported their health was excellent = 44 %

The probability of excellent health P = 0.44

The probability of not excellent health = Q - 1 - 0.44 - 0.56

Since, 14 adults are randomly selected.

To find the probability that 3 or fewer are in excellent health,

Use formula

Probability = [tex]^nC_rP^n Q^{n-r}[/tex]

Where P = probability to happen an event, and Q= probability to not happen an event.

The probability that 3 or fewer are in excellent health

= [tex]^{14}C_3 (0.44)^3(0.56)^{14-3} +^{14}C_2(0.44)^2(0.56)^{14-2}+^{14}C_1 (0.44)^1(0.56)^{14-1} + ^{14}C_0 (0.44)^0(0.56)^{14}[/tex]

= 0.0526 + 0.0167 + 0.00328 + 0.000298

= 0.072282

The required probability is 0.072282.

To know more about Probability on:

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Answer:

There are 45 dogs, 27 cats

Step-by-step explanation:

Write and solve an equation of ratios.  The "cat ratio" is 3/27 and the "dog ratio" is 5/d:

Then

 3         5

------ = -----

 27       d

Through cross-multiplication, we get 3d = 135, or d = 45

There are 45 dogs, 27 cats.  Notice that 27/45 = 3/5, as expected.

There are 45 dogs and 27 cats.  

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Given information;The ratio of cats to dogs at the animal shelter is 3 to 5.

There are 27 cats.

We need to Write and solve an equation of ratios.  

The "cat ratio" is 3/27 and the "dog ratio" is 5/d:

Then 3/ 27 =   5 / d

Through cross-multiplication, we get

d = 5 x 27 / 3d = 45So,

Notice that 27/45 = 3/5, as expected.

There are 45 dogs and 27 cats.  

Learn more about the unitary method;

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Answer:

$304,853

Step-by-step explanation:

Given:

I - 8

N - 10

PMT - 35,000

FV - 0

solution :

We use the Budget method to estimate the amount of insurance needed

PV of annual expenses

=PV(8%,10,-33100) considering Rate=8%, N=10

 PV - ? = $337,501.61

Amount of Insurance to Purchase = $234,853 + $40,000 + $30,000 = $304,853

Answer

You need to pay $14.20 to get 4 coffees and 6 donuts.

Explanation

Let's say that the price of one coffee and x and the price of one donut is y.

In the first instance, 3x+4y=10.05.

In the second instance, 5x+7y=17.15.

You can use these equations to find the value of a coffee and the value of a donut.

We can find x and y using elimination. To do this, you should add or subtract one equation from another to "get rid" of a variable (I'll "get rid" of x). We can't just add or subtract the equations right now, since that wouldn't lead to 0x.

Multiply the first equation by 5, and the second equation by 3. After this, both equations will have 15x. Make sure to multiply each term by 5 and 3.

15x+20y=50.25. This means that 15 coffees and 20 donuts is $50.25.

15x+21y=51.45. This means that 15 coffees and 21 donuts is 51.45.

Now since there are an equal number of coffees, we can subtract these equations.

(15x+21y=51.45)-(15x+20y=50.25) equals y=1.20 (a donut costs $1.20).

Plug the price of the donut into y to find x; 3x+4(1.20)=10.05. The value of x is 1.75. The price of a coffee is 1.75.

You can multiply 1.75 by 4 to find the price of 4 coffees and 1.20 by 6 to find the price of 6 donuts.

1.75*4 is 7.00 and 1.20*6 is 7.20.

You can add those to find the total price; 7.00+7.20=14.20.

Answer:

6) 6[tex]\sqrt{2}[/tex]

9) 40

10) [tex]\frac{5\sqrt{2} }{2}[/tex]

11) 13

Step-by-step explanation:

6)A right triangle rule: if 2 legs are equal, the hypotenuse is the length of that leg*[tex]\sqrt{2}[/tex]

9) Pythagorean Theorem

[tex]a^{2} +b^{2} =c^{2}[/tex]

We know the hypotenuse (41) so we substitute that for c and 9 for b now we need to find a

[tex]\sqrt{41^{2}-9^{2} }[/tex] which gives us 40

10) same with #6 but we do the opposite. SInce we have the hypotenuse, we can divide that by [tex]\sqrt{2}[/tex] because we know that if 2 legs are equal, the hypotenuse is multiplied by [tex]\sqrt{2}[/tex]. Multiply the numerator and denominator by [tex]\sqrt{2}[/tex] because we can't have a square root in the denominator.

11) like #9 we have the a and b but we need to find c

a=5 b=12 c=r

so [tex]\sqrt{5^{2}+12^{2} }[/tex] which gives us 13

[tex] {h}^{2} = {p}^{2} + {b}^{2} [/tex]

[tex] {c}^{2} = {6}^{2} + {6}^{2} \\ {c}^{2} = 36 + 36 \\ c = \sqrt{2( {6}^{2} )} \\ c = \sqrt{2}{\sqrt{ {6}^{{2}} } } \\ c = 6 \sqrt{2} \: \: \: ans[/tex]

SOLUTION->

[tex] {h}^{2} = {p}^{2} + {b}^{2} [/tex]

[tex] {41}^{2} = {x}^{2} + {9}^{2} \\ 1681 = {x}^{2} + 81 \\ 1681 - 81 = {x}^{2} \\ 1600 = {x}^{2} \\ x = \sqrt{40 \times 40} \\ x = 40 \: \: \: ans[/tex]

GIVEN

[tex]{h}^{2} = {p}^{2} + {b}^{2} [/tex]

[tex] {5}^{2} = {s}^{2} + {s}^{2} \\ 25 = 2 {s}^{2} \\ 12.5 = {s}^{2} \\ \sqrt{12.5} = s \\ 3.5 = s \: \: \: ans[/tex]

[tex] {h}^{2} = {p}^{2} + {b}^{2} [/tex]

[tex] {r}^{2} = {12}^{2} + {5}^{2} \\ {r}^{2} \\ 144 + 25 \\ {r}^{2} = 169 \\ r = \sqrt{13 \times 13} \\ r = 13 \: \: \: \: ans[/tex]

HOPE IT HELPED

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \star \: DEVIL005 \: \star[/tex]

Answer:

x^16 y^8

Step-by-step explanation:

x = 8 x 2 = 16

y = 4 x 2 = 8

Answer:

x^16y^8

Step-by-step explanation:

all you gotta do is multiply the exponent on the inside and the outside

hope this helped ^^

Answer:

96

Step-by-step explanation:

Answer:

0.05, 8%, 15/100, 3/10, 0.7

Step-by-step explanation:

so they are 5%, 8%, 15%, 30%, 70%

Answer:

0.0016 = 0.16% probability that the lot will pass inspection.

Step-by-step explanation:

For each bulb, there are only two possible outcomes. Either it is defective, or it is not. The probability of a bulb being defective is independent of any other bulb, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

Sample of 18 light bulbs

This means that [tex]n = 18[/tex]

30% of the bulbs in the lot are defective.

This means that [tex]p = 0.3[/tex]

What is the probability that the lot will pass inspection?

It will pass inspection if there are no defective bulbs, that is, we have to find P(X = 0). So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{18,0}.(0.3)^{0}.(0.7)^{18} = 0.0016[/tex]

0.0016 = 0.16% probability that the lot will pass inspection.

9514 1404 393

Answer:

  (b)  AB overbar congruent to CD overbar

Step-by-step explanation:

AB with an overbar is the way that line segment AB is designated, where appropriate typesetting is possible. Thus the statement the line segments are congruent is fully equivalent to ...

  AB overbar congruent to CD overbar

Answer:

yeah, teachers kinda suck

X = (18/5)/(3/2)

= 18/5 x 2/3

=(18 x 2) / (5x3)

= 90/15

If you don’t want it as a fraction it’s 6!

Hope this helps!

Answer:

3 =f

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan theta = opp/ adj

tan 60 = f/ sqrt(3)

sqrt(3) tan 60 = f

sqrt(3) * sqrt(3) = f

3 =f

Answer:

61 sales

Step-by-step explanation:

First find the increase

45 * 35%

45*.35

15.75

Add this to your sales

45+15.75

60.75

Since you cannot have part of a sale, round up

61 sales

Answer:

6x+y

Step-by-step explanation: