A rectangular fish tank is 50 cm​ long, 40 cm​ wide, and 20 cm high. ​a) How many cubic centimeters of water will the tank​ hold? ​b) How many milliliters of water will the tank​ hold? ​c) How many liters of water will the tank​ hold?

The angle of elevation of the sun when a 10-foot tree creates a shadow that is 15 feet long  is 33.69 degrees

To find the angle of elevation of the sun, we can use trigonometry and the concept of similar triangles.

Given that:

The tree's height is 10 feet.

The length of the shadow is 15 feet.

Let's assume that the tree's height is "h"  feet.

Length of its shadow is represented by "s" feet

The angle of elevation of the sun is the angle between the ground and the line from the top of the tree to the tip of its shadow.

The angle can be determined using the tangent function.

[tex]tan\theta[/tex] = [tex]\dfrac{h}{s}[/tex]

Now, substitute the given values:

[tex]tan\theta[/tex]= [tex]\dfrac{10}{15}[/tex]

[tex]tan\theta[/tex] = [tex]\dfrac{2}{3}[/tex]

The angle of elevation can be obtained by  taking the inverse tangent of 2/3

angle of elevation =[tex]\tan^-1\dfrac{2}{3}[/tex]

angle of elevation ≈ 33.66 degrees

So, the angle of elevation of the sun is approximately 33.69 degrees.

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Answer:

B.

Step-by-step explanation:

In the attached file

Answer:

Step-by-step explanation:

Let X denote the life span of a car battery and it follows and exponential distribution with average of 6 years.

Thus , the parameter of the exponential distribution is calculated as,

μ = 6

[tex]\frac{1}{\lambda} =6[/tex]

[tex]\lambda = \frac{1}{6}[/tex]

a) The required probability is

[tex]P(X>4)=1-P(X\leq 4)\\\\=1-F(4)\\\\1-(1-e^{- \lambda x})\\\\=e^{-\frac{4}{6}[/tex]

= 0.513

Hence, the probability that a randomly selected car battery will last more than four years is 0.513

b) The variance of the battery span is calculated as

[tex]\sigma ^2=\frac{1}{(\frac{1}{\lambda})^2 }\\\\\sigma ^2=\frac{1}{(\frac{1}{6})^2 } \\\\=6^2=36[/tex]

The 95% percentile [tex]x_{a=0.05}[/tex] (α = 5%) of the battery span is calculated

[tex]x_{0.05}=-\frac{log(\alpha) }{\lambda} \\\\=-\frac{log(0.05)}{1/6} \\\\=-6log(0.05)\\\\=17.97 \ years[/tex]

c)  

Let [tex]X_r[/tex] denote the remaining life time of a car battery

i)the probability the battery will last an additional five years is calculated below

[tex]P(X_r>5)=e^{-5\lambda}\\\\=e^{-\frac{5}{6} }\\\\=0.4346[/tex]

ii) The average time that the battery is expected to last is calculated

[tex]E(X_r)=\frac{1}{\lambda} \\\\=6[/tex]

Answer:

19.2

Step-by-step explanation:

It's right on Acellus.

The required value of x nearest to tenth is 19.17

The longest side of the right angled triangle is called hypotenuse

By the Pythagoras theorem in the right angled triangle

h^2 = b^2 + p^2

where h = hypotenuse, b = base, p = perpendicular

Here we have given perpendicular p = 9

and an angle = 28°

Using sin for the given angle we have

sin 28° = [tex]\frac{perpendicular}{hypotenuse}[/tex]

0.46947 = [tex]\frac{9}{x}[/tex]

x = [tex]\frac{9}{0.46947}[/tex]

x =  19.17

Hence the required length of the side hypotenuse = x = 19.17

This is the conclusion to the answer.

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Answer:

The expected value of the random variable with the given probability distribution = 12 .52

Step-by-step explanation:

Given data

 x    :   0         1            5       10     1000

p(x)  :  0.33  0.32   0.24     0.10    0.01

The expected value of the given random variable of given probability distribution

E(X)  =  ∑ x p ( X = x)

E(X)  =  0 × 0.33 + 1 × 0.32 + 5 × 0.24 + 10× 0.10 + 1000×0.01

E (X)  =  12.52

Answer:

the Swiss Chalet had higher occupancy than its competitive set in 2019

Step-by-step explanation:

Answer:

The percentage of the employee will experience a lost-time accident in both years is 0.0%

Step-by-step explanation:

Let A denote events that employees suffered lost-time accidents during the last year

Let B denote events that employees suffered lost-time accidents during the current year

P(A) = 5% = 0.05

P(B) = 4% = 0.04

P(B | A) = 15% = 0.15

(a) P (A ∩ B) = P(B | A) × P(A)

= 0.15 × 0.05

= 0.0075

= 0.0 (1 decimal place)

The probability that an employee will experience a lost- time accident in both years is 0.0

Answer:

[tex]P(X<3) =[/tex] [tex]0.9619[/tex]

Step-by-step explanation:

From the given information;

the probability of getting returned p = 0.1

If eight rings are sold today, what is the probability that fewer than three will be returned;

According to binomial distribution

Binomial distribution is the probability of success or failure of an outcome of an experiment under observation which is usually repeated several trials. Binomial experiments are random experiment with fixed number of repeated experiment. If we cannot predict before head, the outcome of an experiment , the experiment is called a random experiment.

So , using binomial distribution to determine the probability that fewer than three will be returned;

i.e

[tex]P(X<3) =[/tex] [tex]\sum_{x=0}^{2}\binom{8}{x}(0.1)^{x}(1-0.1)^{8-x}[/tex]

[tex]P(X<3) =[/tex] [tex]0.9619[/tex]

Answer:

FALSE

Step-by-step explanation:

Answer:

0.45

Step-by-step explanation:

9/20 is the same as 0.45

Answer:

0.45

Step-by-step explanation:

9/20= 9*5/20*5= 45/100= 0.45

Answer:

72°

Step-by-step explanation:

This is called an isosceles triangle. This means that the 2 angles related to the equal sides, are also equal. Hence, the answer is 72°

Answer:

A

Step-by-step explanation:

Since it is isosceles triangle (two equal sides) therefore, there are 2 equal angles too which at the base (72°)

The total angle of triange is 180°

So 180-72-72=36°

Answer:

x = -6

Step-by-step explanation:

-2/3x + 9 = 4/3x - 3

First we need to simplify to where we have x on one side and a constant (number not connected to a variable) on the other side.

Subtract 4/3x from both sides:

-2/3x + 9 - 4/3x = -3

-6/3x + 9 = -3

Now subtract 9 from both sides:

-6/3x + 9 - 9 = -3 - 9

-6/3x = -12

Now turn -6/3 into a whole number to make things more simple:

-6/3 = -2

-2x = -12

Now divide both sides by -2 to get x by itself

-2x/-2 = -12/-2

x = -6

Answer:

A

Step-by-step explanation:

It is not B because 7x^2 means multiplying the equation by seven. It isn't C because that would move the graph DOWN seven units. And it's not D because when it is in parenthesis like that, it means that it is a horizontal shift, not vertical.

Answer:

A. G(x) = [tex]x^2+7[/tex]

Step-by-step explanation:

→For the function to shift upwards 7 units, 7 must be added to the function, like so:

G(x) = [tex]x^2+7[/tex]

→F(x) + c (in this case is 7), cases a vertical shift and the function is moved "c," units. The graph would shift downwards if 7 was being subtracted.

This means the correct answer is A.

The slope is zero. Slope formula is Y=mx+b and since B is 1.5 and it is a straight line, Y=mx+1.5. What plus 1.5 is 1.5? 0. Hope this helps.

Answer:

D

Step-by-step explanation:

(eˣ − e⁻ˣ) / (eˣ + e⁻ˣ) = t

Multiply by eˣ/eˣ.

(e²ˣ − 1) / (e²ˣ + 1) = t

Solve for e²ˣ.

e²ˣ − 1 = (e²ˣ + 1) t

e²ˣ − 1 = e²ˣ t + t

e²ˣ = 1 + e²ˣ t + t

e²ˣ − e²ˣ t = 1 + t

e²ˣ (1 − t) = 1 + t

e²ˣ = (1 + t) / (1 − t)

Solve for x.

2x = ln[(1 + t) / (1 − t)]

x = ½ ln[(1 + t) / (1 − t)]

Use log rule.

x = ln(√[(1 + t) / (1 − t)])

Answer:

I think it is -2

Step-by-step explanation:

I think but I do not know

Answer:

the answer is E the number at the top tells you which position it falls under in the alphabet

Answer:

C. can have more than one factor, each with several treatment groups.

Step-by-step explanation:

A completely randomized design can be used in experimental research of a primary factor or multiple factors. The factors could have several treatment groups which are assigned in a random manner. For example, a researcher, could want to determine the effect of a drug against a disease on a class of people. To do this, he designs a treatment group with different concentrations of the drug and a placebo group. He then gets an equal number of subjects, randomly assigning them to each of the groups. The effect of both treatments are compared to know if the drug is indeed effective against the disease the researcher is experimenting on.

Completely randomized design has found application in agricultural and environmental researches.

Answer:

[tex]\frac{a^3 b^2}{\frac{1}{a} \frac{1}{b^3}}[/tex]

And simplifying we got:

[tex] a^3 b^2 a b^3[/tex]

[tex] a^3 a b^2 b^3 = a^{3+1} b^{2+3} = a^4 b^5[/tex]

Step-by-step explanation:

We want to simplify the following expression:

[tex] \frac{a^3 b^2}{a^{-1} b^{-3}}[/tex]

And we can rewrite this expression using this property for any number a:

[tex] a^{-1}= \frac{1}{a}[/tex]

And using this property we have:

[tex]\frac{a^3 b^2}{\frac{1}{a} \frac{1}{b^3}}[/tex]

And simplifying we got:

[tex] a^3 b^2 a b^3[/tex]

[tex] a^3 a b^2 b^3 = a^{3+1} b^{2+3} = a^4 b^5[/tex]

Answer:

your number should be 8

Step-by-step explanation:

5x+(-3)=37

5x-3=37

+3       +3

5x=40

÷5  ÷5

x=8

hope this helps

Answer:

The answer is 8.

5x-3=37

5x=37+3

5x=40

x=40/5

x=8

HOPE IT HELPS!!

Answer:

Yes

Step-by-step explanation:

the function that gives the alcohol level is:

[tex]A ( x ) = - 0.015 x^3 + 1.05 x[/tex]

where x is the number of hours.

we need to know if after 4 hours an average person is legally drunk, thus:

[tex]x=4[/tex]

and we substitute this in the function:

[tex]A ( 4 ) = - 0.015 (4)^ 3 + 1.05(4)[/tex]

solving these operations we obtain:

[tex]A(4)=-0.015(64)+4.2\\A(4)=-0.96+4.2[/tex]

[tex]A(4)=3.24[/tex]

the alcohol level after 4 hours is 3.24.

Since a person is considered to be legally drunk if the level exceeds 1.5, and we obtained 3.24 which is greater than 1.5, a person who has been drinking for 4 hours under the conditions indicated by the problem would be considered legally drunk.

Answer:

A) 50 km : 45 km : 65 km

B) 18:45:3

Step-by-step explanation:

A) 160 km in the ratio 10:9:13

10:9:3 ⇔ 50 km : 45 km : 65 km

B) 66 in the ratio 6:15:1

6:15:1  ⇔ 18:45:3

Answer: 880 oz

Step-by-step explanation:

We want to write it in the same units, let's use oz as our common unit.

1 gal = 128 oz

then 5 gal = 5*128 oz = 640 oz

1 qt = 32 oz

then 6 qt = 6*32 oz = 192 oz

Then we have:

640 oz + 192 oz + 48 oz = 880 oz

The value of standard notation is,

⇒ 880 oz

We have to given that,

Measures are,

⇒ 5 gal 6qt 48 oz

We have to change it into standard notation as,

We want to write it in the same units, let's use oz as our common unit.

1 gal = 128 oz

then 5 gal = 5 x 128 oz = 640 oz

1 qt = 32 oz

then 6 qt = 6 x 32 oz = 192 oz

Then we have:

⇒ 5 gal 6qt 48 oz

⇒ 640 oz + 192 oz + 48 oz

⇒ 880 oz

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As the x values go up, the y values go down which means the line is higher on the left side than it is on the right side.

The 4th graph would be the correct one

Question Correction

A group of neighbors are constructing a community garden that is 80 meters wide and 40 meters long. The top two vertices are plotted below at (10, 70) and (90, 70). What are the coordinates for the bottom two vertices of the garden?

Answer:

(10,30) and (90,30)

Step-by-step explanation:

The community garden is 80 m wide and 40 m long.

The top two vertex are plotted at: (10, 70) and (90, 70).

Horizontal Distance =90-10=80

This serves as the Width of the garden.

Since the length is 40m, the bottom two vertex can be derived by the transformation: (x,y-40).

(x,y-40)-->(10, 70)=(10,30); and

(x,y-40)-->(90, 70)=(90,30)

The coordinates for the two bottom vertices are (10,30) and (90,30).

Answer:

x=-21

Step-by-step explanation:

x+12=-9

minus twelve on both sides

-9-12 equals -21

x=-21

Answer:

96

Step-by-step explanation:

Rectangle area:

(8)(10)=80

Triangle area:

(1/2)(4)(8)=16

Total area:

16+80=96

Answer:

[tex]96 {ft}^{2} [/tex]

Step-by-step explanation:

[tex]area = \frac{1}{2} (a + b)h \\ = \frac{1}{2} \times (10 + 14) \times 8 \\ = \frac{1}{2} \times 24 \times 8 \\ = 96 {ft}^{2} [/tex]

Answer:

  24

Step-by-step explanation:

Let t represent the volume of the tank in gallons. Then we have ...

  (1/8)t + 15 = (3/4)t . . . . . . . . . . . adding 15 gallons fills the tank to 3/4

  15 = (6/8 -1/8)t = (5/8)t . . . . . . . subtract 1/8t

  15(8/5) = (8/5)(5/8)t . . . . . . . . . multiply by 8/5 (the inverse of 5/8)

  24 = t

The tank holds 24 gallons.