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?

Complete Question

A box is formed by cutting squares from the four corners of a sheet of paper and folding up the sides. However, the size of the paper is unknown!

Answer:

(a)[tex]f(0.2)=0.2(l-0.4)(w-0.4)[/tex]

(b)[tex]f(1.3)=1.3(l-2.6)(w-2.6)[/tex]

(c)f(1.3)-f(0.2)

(d) f(5.6)-f(5.5)

Step-by-step explanation:

Let the Length of the paper =l  (in inches)

Let the Width of the paper =w  (in inches)

Let the length of the cutout square = x (in inches)

Volume of the box: [tex]f(x)=x(l-2x)(w-2x)[/tex]

(a)When the cutout length is 0.2 inches.

x=0.2

Volume of the box (in cubic inches) ,

[tex]f(0.2)=0.2(l-0.4)(w-0.4)[/tex]

(b)When the cutout length is 01.3 inches.

x=1.3

Volume of the box (in cubic inches) ,

[tex]f(1.3)=1.3(l-2.6)(w-2.6)[/tex]

(c)If the cutout length increases from 0.2 inches to 1.3 inches.

Change In volume (in cubic inches):

[tex]f(1.3)-f(0.2)\\=1.3(l-2.6)(w-2.6)-0.2(l-0.4)(w-0.4)[/tex]

(d)If the cutout length increases from 5.5 inches to 5.6 inches.

Change In volume (in cubic inches):

[tex]f(5.6)-f(5.5)\\=5.6(l-11.2)(w-11.2)-5.5(l-11)(w-11)[/tex]

Answer:

dose in MCG = 10.2 mcg

Total volume to be sent home = 1.836 ml (1836μl)

Step-by-step explanation:

weight of patient = 680g

dosage in mcg of medication = 15mcg/kg

This means that

for every 1kg weight, 15mcg is given,

since 1kg = 1000g, we can also say that for every 1000g weigh, 15mcg is given.

1000g = 15mcg

1g = 15/1000 mcg = 0.015 mcg

∴ 680g = 0.015 × 680 = 10.2 mcg

Dosage in MCG = 10.2 mcg

Next, we are also told ever ml volume of the drug contains 50 mcg weight of the drug (50mcg/ml). This can also be written as:

50mcg = 1 ml

1 mcg = 1/50 ml = 0.02 ml

∴ 10.2 mcg = 10.2 × 0.02 = 0.204 ml

since the medication is to be taken TID (three times daily) for 3 days, the total number of times the drug is to be taken = 9 times.

therefore, the total volume required = 0.204 × 9 = 1.836 ml (1836 μl)

Answer:

The percentage would be 20% (5x20=100)

Step-by-step explanation:

Answer:

Step-by-step explanation:

a)4a-6a                   d)2x+4y-10x

   =-2a.                     =-8-+4y

b)14-1-10

=3

c)2+8

=10

e)answer is 6 x raised to the power 3

f)7x raised to the power 2-5x-y

Answer:

Option D

Step-by-step explanation:

This question is based on the " Partition Postulate. " You might be familiar with it, it states that a whole is composed of several parts. In this case you could say that this " whole " is ∠ ABC, and the " parts " are ∠1 and ∠2. By this Theorem you could also state the following;

[tex]m< ABC = m< 1 + m< 2,\\\\Substitute,\\110 = 4x + ( 5x + 10 ),\\110 = 4x + 5x + 10,\\4x + 5x + 10 = 110 - Option D\\\\Solution - Option D[/tex]

Hope that helps!

Answer:

157.6

Step-by-step explanation:

Use PEMDAS! In this rule, it is stated that we should always add/subtract before multiplying/dividing. Also, whatever you do on one side of an equation, you do to another. Therefore, in order to get rid of the -2/5, add 2/5 so we can get rid of it. We also (according to the rule), have to add it to the other side in order to balance out. So add the 2/5 to 39. Then the other side is now 39.4. Now we have to get x by itself. Divide both sides by 1/4 (or multiply by 4 on both sides) in order to get x=157.6

Answer:

C:

Step-by-step explanation:

Both angles add up to 180°

<BCG + <BFG = 180°

2x+146+4x+238=180

6x+384 = 180°

6x = 180-384

6x = -204

Dividing both sides by 6

x = -34

Hey there! I'm happy to help!

The only thing we have to do is solve our inequality to find the answer!

30+15x ≥ 90

We subtract 30 from both sides.

15x ≥ 60

Finally, we divide both sides by four.

x ≥ 4

Therefore, Deepak can only accept jobs that last 4 or more hours.

I hope that this helps! Have a wonderful day!

The solution for the inequality is x≥4. Therefore, option A is the correct answer.

Given that, Deepak is a landscaper who charges $30 for each job he does plus an additional $15 for each hour he works.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

The inequality for the given situation is 30+15x≥90

Subtract 30 on the both the sides of an inequality, which is

30+15x-30≥90-30

⇒ 15x≥60

Divide 15 on the both the sides of an inequality, that is

15x/15≥60/15

⇒ x≥4

The solution for the inequality is x≥4. Therefore, option A is the correct answer.

To learn more about the inequalities visit:

https://brainly.com/question/20383699.

#SPJ5

Answer:

Options A, B and E are correct

Step-by-step explanation:

From the information given above, we would draw a dilation that produces an image that is the same shape as the original image, but has a different size.

The scale factor is 2

QRS → Q'R'S' = (x,y) → 2(x,y)

The coordinates of ∆QRS

Q (-3, 3)

R (2, 4)

S (-1, 1)

To get the coordinates of Q'R'S', we would multiply each coordinate of the original triangle by the scale factor of 2 since the dilation is from the origin. In order words, each vertex of QRS is multiplied by 2 to get each of the vertex of Q'R'S'.

2 (x,y) = (2x, 2y)

The coordinates of ∆Q'R'S' becomes:

Q' (-6, 6)

R' (4, 8)

S' (-2, 2)

To determine the statements that are true about the image ΔQ'R'S,

we would graph the coordinates of the two triangles.

Starting with ΔABC, we would draw the dilation image of the triangle with a center at the origin and a scale factor of 2.

See attached the diagram for better explanation.

Let's check out each options and compare it with diagram we obtained:

a) DO, 2 (x,y) = (2x, 2y)

A dilation about the origin with a scale factor 2 is described using the above notation.

Q' = 2(-3,3) = [2(-3), 2(3)] = (-6, 6)

R' (4, 8) = 2(2,4) = [2(2), 2(4)] = (4, 8)

S' (-2, 2) = 2(-1,1) = [2(-1), 2(1)] = (-2, 2)

This option is correct

b) Side Q'S' lies on a line with a slope of -1

Q' (-6, 6)

S' (-2, 2)

coordinate (x, y)

Slope = m = (change in y)/(change in x)

m = (6-2)/[-6-(-2)]

= 4/(-6+2) = 4/-4

m = -1

This option is correct

c) QR is longer than Q'R'

Length of QR (-3 to 2) = 5

Length of Q'R' (-6 to 4) = 10

QR is not longer than Q'R'

This option is false

d) The vertices of the image are closer to the origin than those of the pre-image

The scale factor determines how much bigger or smaller the dilation image will be compared to the preimage. In a transformation, the final figure is referred to as the image. The original figure is referred to as the preimage.

From the diagram, the vertices of the preimage (original image) are closer to the origin than those of the dilation image.

This option is false

e) The distance from Q' to the origin is twice the distance from Q to the origin.

The distance from Q' to the origin (6 to 0) = 6

The distance from Q to the origin (3 to 0) = 3

The distance from Q' to the origin = 2(the distance from Q to the origin)

This option is correct

Answer:

A,B and E is correct

Step-by-step explanation:

Answer:

(x-2)(x-2)

Step-by-step explanation:

You should be trying to find two numbers that add to make the coefficient of x (in this case, -4), and two numbers that multiply to make the constant term (in this case, +4). The two numbers that work for both of those criteria are -2 and -2.

-2 x -2 = +4 (satisfies the constant term)

-2 + -2 = -4 (satisfies the coefficient of x)

Answer:

A. Observational study

Step-by-step explanation:

In research, an observational study is a type of study in which the researcher observes a phenomenon and tries to establish some relationship between the different variables he/she is observing. In other words, the researcher only observes and doesn't give a treatment.

On the other hand, when we have a experiment, we usually have 2 different groups (one that will receive a treatment and one who won't) and the researcher compares the differences between these two groups because of the treatment. In other words, the researcher does something other than just observing.

In this example, the research is going to determine if there is a relation between hearing loss and exposure to mumps. In this example the researcher is only going to observe how people who have been exposed to mumps are regarding hearing loss (we can say this since it will be unethical for example for the researcher to create an experiment in which he/she exposes a group to mumps). Therefore, he is going to observe how the past exposure to mumps could be related with the hearing loss.

Thus, this is an observational study.

Answer:

The speed of the river is 2mph.

Step-by-step explanation:

I guess that we want to find the speed of the river.

First, remember the relation: speed*time = distance

If the speed of the river is Sr, when Luvenia moves downstream (in the same direction that the flow of the water) the total speed will be equal to the speed of Luvenia in still water plus the speed of the water:

Sd = 4mph + Sr

and at this speed, in a time T, she can move 21 miles, so we have:

Sd*T = (4mph + Sr)*T = 21 mi

When moving upstream, the speed will be:

Su = (4mph - Sr)

and in the same time T as before, she moves 7 miles, so we have the equation:

Su*T = (4mph - Sr)*T = 7 mi

Then we have two equations:

(4mph + Sr)*T = 21 mi

(4mph - Sr)*T = 7 mi

Now we can take the quotient of those two equations and get:

((4mph + Sr)*T)/((4mph - Sr)*T) = 21/7

The time T vanishes, and we can solve it for Sr.

(4mph + Sr)/(4mph - Sr) = 3

4mph + Sr = 3*(4mph - Sr) = 12mph - 3*Sr

4*Sr = 12mph - 4mph = 8mph

Sr = 8mph/4 = 2mph.

Answer:

f(1/2)=1.5

f(1/4)=0.75

Answer and Step-by-step explanation:

The computation of annual and quarterly mortality rates per 100,000 population is shown below:-

Quarterly mortality rates are

[tex]= \frac{Deaths}{Population\ in\ the\ city}\times Population[/tex]

For the first quarter

[tex]= \frac{54}{450,000}\times 100,000[/tex]

= 12  death per 100,000 population

For the second quarter

[tex]= \frac{43}{450,000}\times 100,000[/tex]

= 9.5  death per 100,000 population

For the third quarter

[tex]= \frac{35}{450,000}\times 100,000[/tex]

= 7.7  death per 100,000 population

For the fourth quarter

[tex]= \frac{39}{450,000}\times 100,000[/tex]

= 8.6  death per 100,000 population

Now the annual mortality is

[tex]= \frac{Deaths}{Population\ in\ the\ city}\times Population[/tex]

[tex]= \frac{171}{450,000}\times 100,000[/tex]

= 38 death per 100,000 population

Answer:

[tex] z=\frac{510-520}{\frac{90}{\sqrt{100}}}= -1.11[/tex]

And we can find the probability using the normal standard distribution table and with the complement rule we got:

[tex]P(z<-1.11)= 0.1335[/tex]

Step-by-step explanation:

For this problem we have the following parameters:

[tex] \mu = 520, \sigma = 90[/tex]

We select a sample size of n =100 and we want to find this probability:

[tex] P(\bar X <510) [/tex]

The distribution for the sample mean using the central limit theorem would be given by:

[tex]\bar X \sim N(\mu,\frac{\sigma}{\sqrt{n}})[/tex]

And we can solve this problem with the z score formula given by:

[tex] z=\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

And if we find the z score formula we got:

[tex] z=\frac{510-520}{\frac{90}{\sqrt{100}}}= -1.11[/tex]

And we can find the probability using the normal standard distribution table and with the complement rule we got:

[tex]P(z<-1.11)= 0.1335[/tex]

Answer:

  D  0.00009

Step-by-step explanation:

9 × 10^-5 = 9 × 1/10^5 = 9 × 1/100,000

  = 9 × 0.00001

  = 0.00009

_____

Comment on place value

The exponent of 10 associated with the place value in a decimal number increases from 0 to the left of the decimal point, and decreases from -1 to the right of the decimal point:

  100. = 10²

  10. = 10¹

  1. = 10⁰

  0.1 = 10⁻¹

  0.01 = 10⁻²

  0.001 = 10⁻³

  0.0001 = 10⁻⁴

  0.00001 = 10⁻⁵

This simple realization can help you immensely with scientific notation.

Answer:

15.86%

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Percent of area between the mean and 0.20 standard deviations from the mean:

pvalue of Z = 0.2 subtracted by the pvalue of Z = -0.2

Z = 0.2 has a pvalue of 0.5793

Z = -0.2 has a pvalue of 0.4207

0.5793 - 0.4207 = 0.1586

So this percentage is 15.86%

Answer:

1. Due to the lower standard deviation, it is more likely to obtain a sample of females within $10,000 of the population mean

2. 15.87% probability that a simple random sample of 100 male graduates will provide a sample mean more than $4,000 below the population mean

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

1. In which of the preceding two cases, part a or part b, do we have a higher probability of obtaining a smaple estimate within $10,000 of the population mean? why?

The lower the standard deviation, the less dispersed the values are, meaning it is more likely to find values within a certain threshold of the mean.

So

Due to the lower standard deviation, it is more likely to obtain a sample of females within $10,000 of the population mean.

2. What is the probability that a simple random sample of 100 male graduates will provide a sample mean more than $4,000 below the population mean?

We have that:

[tex]\mu = 168000, \sigma = 40000, n = 100, s = \frac{40000}{\sqrt{100}} = 4000[/tex]

This probability is the pvalue of Z when X = 168000 - 4000 = 164000. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{164000 - 168000}{4000}[/tex]

[tex]Z = -1[/tex]

[tex]Z = -1[/tex] has a pvalue of 0.1587

15.87% probability that a simple random sample of 100 male graduates will provide a sample mean more than $4,000 below the population mean

Answer:

368

Step-by-step explanation:

Answer:

46/ 67

Step-by-step explanation:

The numbers of students irrespective of grades is;

The sum of the last roll of numbers:

10+24+ 33+ 67 = 134

The number of males irrespective of grades is the sum of the numbers in the male row ;

7 +20+ 14 +41= 82

The numbers of students with grade A is the first column at the last row and is 10;

Hence;

the probability that the student was male OR got an 'A' is

the probability that the student was male plus the probability that he/she got an 'A'.

The probability that it's a male is ;

Number of males/ total number of students

=82/134

The probability that he got an A is;

The number of students that got A/ the total number of students;

10/134

Hence

the probability that the student was male OR got an 'A' is;

82/ 134 + 10/134 = 92/134 = 46/ 67

Answer:

0

Step-by-step explanation:

In a suit of 52 cards

The experiment consists of drawing 1 card from the standard deck.

Since diamonds are red, there is no black jack of diamonds.

Therefore:

P(drawing a black jack of diamonds)

[tex]=\dfrac{0}{52}\\\\ =0[/tex]

Answers:

In photo below

Explanation:

I got it correct in my test :)

Answer:

i

Step-by-step explanation:

Why is i the square root of negative one?

The term "imaginary" is used because there is no real number having a negative square. There are two complex square roots of −1, namely i and −i, just as there are two complex square roots of every real number other than zero, which has one double square root.

Answer:

4.700

Step-by-step explanation:

Find the number in the thousandth place  0  and look one place to the right for the rounding digit 4. Round up if this number is greater than or equal to 5 and round down if it is less than 5.

brainliesssss plssssssssssssss

Answer:

slope = 3/2

Step-by-step explanation:

3x-2y=6

Get this equation in the form y = mx+b where m is the slope and b is the y intercept

Subtract 3x from each side

3x-3x-2y=-3x+6

-2y = -3x+6

Divide each side by -2

-2y/-2 = -3x/-2 +6/-2

y = 3/2x -3

The slope is 3/2 and the y intercept is -3

Answer:

3/2

Step-by-step explanation:

I got this answer by putting it in the form y=mx+b

Step 1: Subtract 3x from each side

-2y = -3x+6

Step 2: Divide each side by -2

y = 3/2x -3

The slope is 3/2 and the y intercept is -3 because m is the slope and b is the y-intercept.

Answer:

Below.

Step-by-step explanation:

18. Since A is congruent to B, you can conclude that B is congruent to A by the Reflexive Property of Congruence.

Answer:

1651

Step-by-step explanation:

let s say that the price before the increase is x

to apply an increase of 9% it does x + x*0.09 = x*(1+0.09)=x*1.09

and we know that this value is 1800

so

x*1.09=1800

<=>

x = 1800/1.09=1651.376147

to the nearest penny it gives 1651

Answer:

Hello!

Answer: 1651

I hope that was correct.  Please let me know, thank you!

Step-by-step explanation:

Answer:

108

Step-by-step explanation:

9 times 12 is 108

Answer:

(-5, 38) and

(5,18)

Step-by-step explanation:

[tex]x^2-2x+3=-2x+28\\<=> x^2-2x+3+2x=28\\<=> x^2 = 28-3=25\\<=> x^2-25=0\\<=> x^2-5^2 =0\\<=> (x-5)(x+5)=0\\<=> x = 5 \ or \ x=-5[/tex]

so the solutions are

(-5, 38) and

(5,18)

Answer:

The answer is 2

From the function when the input is 2 the output is -7. The inverse reverses the order so the input will be -7 and the output will be 2.

Answer:

Option D is the correct answer.

Step-by-step explanation:

Coefficients od dividend = (4, - 17, - 15)

Dividend [tex]=4x^2 - 17x - 15[/tex]

Divisor x = 5 =>x-5= 0

Coefficients of Quotient = (4, 3)

Quotient [tex]=4x + 3[/tex]

Remainder = 0

Since,

[tex] Dividend = Divisor \times quotient + Remainder\\

\therefore 4x^2 - 17x - 15 = (x - 5)\times (4x + 3) +0 \\

\therefore 4x^2 - 17x - 15 = (x - 5)\times (4x + 3) \\

\therefore( 4x^2 - 17x - 15) \div (x - 5) = (4x + 3)

[/tex]