A public library has an aquarium in the shape of a rectangular prism. The base is 6 feet by 2.5 feet. The height is 4 feet. How many square feet of glass were used to build the aquarium? (The top of the aquarium is open.)

Answer:

The standard error of distribution for n = 4 is 5 and for n = 25 is 2.

Step-by-step explanation:

1. Let's review the information given to us for solving the question:

Population mean = 72

Standard deviation  =  10

Sample₁ = 4

Sample₂ = 25

2. For finding the standard error of the mean, we use the following formula:

Standard error = Standard deviation / √Size of the sample

Standard error for Sample₁ = 10/√4

Standard error for Sample₁ = 10/2 = 5

Now, let's find the standard error for Sample₂

Standard error for Sample₂ = 10/√25

Standard error for Sample₂ = 10/5 = 2

[tex]\bf x^2+4=0\implies x^2=-4\implies x = \pm\sqrt{-4}\implies x = \pm\sqrt{-1\cdot 2^2} \\\\\\ x = \pm\sqrt{-1}\cdot \sqrt{2^2}\implies x = \pm 2i[/tex]

Answer:

3

Step-by-step explanation:

Given: [tex]$  (\frac{1}{4} + \frac{5}{4} )^{2} + \frac{3}{4} $[/tex]

This is equivalent to: [tex]$ ( \frac{6}{4}) ^2 + \frac{3}{4} $[/tex]

⇒  [tex]$ (\frac{3}{2})^2 + \frac{3}{4} $[/tex]

⇒ [tex]$ \frac{9}{4} + \frac{3}{4} $[/tex]

⇒ [tex]$\frac{12}{4} = 3$[/tex]

Therefore,  [tex]$(\frac{1}{4} + \frac{5}{4} )^{2} + \frac{3}{4} = 3 $[/tex]

Answer:

(1/4 + 5/4)^2 +3/4 = 12

Step-by-step explanation:

To solve the problem given, we will follow the steps below;

(1/4 + 5/4)^2 +3/4

First, we will find the value of  (1/4 + 5/4)^2

1/4 + 5/4 = 6/4

(1/4 + 5/4)^2   =   (6/4)^2 =  [tex]\frac{36}{16}[/tex]

 [tex]\frac{36}{16}[/tex]  can be reduced to   [tex]\frac{9}{4}[/tex]

This implies that ; (1/4 + 5/4)^2    =   [tex]\frac{9}{4}[/tex]

Then, we can now add  [tex]\frac{9}{4}[/tex]   and [tex]\frac{3}{4}[/tex]  together  

(1/4 + 5/4)^2 +3/4    =   [tex]\frac{9}{4}[/tex]   +  [tex]\frac{3}{4}[/tex]   =  [tex]\frac{12}{3}[/tex]   = 4

Therefore    (1/4 + 5/4)^2 +3/4 = 12

Answer:

10657.5

Step-by-step explanation:

We can start by finding the area of the larger triangle. Using the Pythagorean theorem, we can say that 251²-105²=the bottom side², and  251²-105²=51976, so the bottom side of the larger triangle is √51976 , or approximately 228. Then, the area of the larger triangle is √51976 * 105/2 = 11969 (approximately). Then, the area of the smallest triangle (the largest triangle - the one that we're trying to find the area of) is 105*(√51976-203)/2 = approximately 1312. Then, subtracting that from the total area, we get (√51976 * 105 -  105*(√51976-203))/2 = 105*203/2 = 10657.5

ALTERNATIVELY, upon further review, we can just see that the height is 105 and the base is 203, so we multiply those two and divide by 2, as is the formula for the area of a triangle, to get 10657.5

Answer:40100 feet

Step-by-step explanation:26400 +13700 = 40100

The total height of Mauna Loa is by summation 26400 +13700 = 40100 feet.

A summation, abbreviated as a sum, is the outcome of adding two or more numbers or quantities. Here are always an integer number of terms in a summation. There could be only two terms, but there could be one hundred, a thousand, or a million.

As per the given,

Initial height = 13700 feet

Height add on = 26400 feet

Total height = 13700 feet + 26400 feet = 40100 feet

Hence "The total height of Mauna Loa is by summation 26400 +13700 = 40100 feet".

For more information about summation

brainly.com/question/10777222

#SPJ2

Answer:

f(x) = (8/3)^x

Step-by-step explanation:

Since f increasing, the base value must be greater than 1.

8/3 is the only base value greater than 1.

The base (3/8) would be a decreasing graph because it is less than 1.

The base (-3/8) would result in a wavering graphing passing the x-axis many times. (Because whether the result is negative depends on if x is odd or even.)

in (8/3)^(-x), it is the same as (3/8)^x by applying the negative exponent rule a^(-x) = 1/(a^x).

Answer:

The distance is 7 (approximately).

Step-by-step explanation:

Given:

Point A, (2,3) and point B, (-4,6).

Now, to find the distance between the points using the formula:

Let A = (2,3) be [tex](x_{1}, y_{1})[/tex] and B = (-4,6) be [tex](x_{2}, y_{2})[/tex] and d = distance.

Putting the distance formula to find:

[tex]d=\sqrt{(x_{2}-x_{1})^{2} +(y_{2}-y_{1})^{2}}[/tex]

[tex]d=\sqrt{(-4-2)^{2} +(6-3)^{2}}[/tex]

[tex]d=\sqrt{(-6)^{2} +(3)^{2}}[/tex]

[tex]d=\sqrt{36 +9}[/tex]

[tex]d=\sqrt{45}[/tex]

[tex]d=6.71[/tex]

Distance = 6.71

Therefore, the distance is 7 (approximately).

If it's Pythagorean Theorem, then use the following:

[tex]A^2 + B^2 = C^2[/tex]

You have to multiply the 2 values by themselves if you are trying to find the Hypotenuse, then you need to add those together, and then find the square root.

10 x 10 = 100

15 x 15 = 225

100 + 225 = 325.

[tex]\sqrt{325} = 18.0277564[/tex]

Answer: 18

Step-by-step explanation:

So this is referencing the Pythagorean theorem. It states that the two shorter sides squared, in your case 10 and 15, is equal to the longest side, or hypotenuse squared.

Step by step

1. Calculate both the shorter sides squared: 10*10= 100 and 15*15= 225

2. Add the 2 shorter sides: 100 + 225 = 325

3. Find the square root of 335: √(325) = 18.0277563773

4. Round to the nearest integer: 18

Answer:

$60

Step-by-step explanation:

75% divided by 100 x 80 = 60

              OR

$80 divided by 100 x 75 = 60

Answer:

[tex]x=0,x=\pi,x=\frac{\pi}{3},x=\frac{2\pi}{3},x=\frac{4\pi}{3},x=\frac{5\pi}{3}[/tex]

Step-by-step explanation:

This is a trigonometric equation where we need to use the cosine of the double-angle formula

[tex]cos4x=2cos^22x-1[/tex]

Replacing in the equation

[tex]cos4x - cos2x = 0[/tex]

We have

[tex]2cos^22x-1 - cos 2x = 0[/tex]

Rearranging

[tex]2cos^22x - cos 2x-1 = 0[/tex]

A second-degree equation in cos2x. The solutions are:

[tex]cos2x=1,cos2x=-\frac{1}{2}[/tex]

For the first solution

cos2x=1 we find two solutions (so x belongs to [0,2\pi))

[tex]2x=0, 2x=2\pi[/tex]

Which give us

[tex]x=0,x=\pi[/tex]

For the second solution

[tex]cos2x=-\frac{1}{2}[/tex]

We find four more solutions

[tex]2x=\frac{2\pi}{3},2x=\frac{4\pi}{3},2x=\frac{8\pi}{3},2x=\frac{10\pi}{3}[/tex]

Which give us

[tex]x=\frac{\pi}{3},x=\frac{2\pi}{3},x=\frac{4\pi}{3},x=\frac{5\pi}{3}[/tex]

All the solutions lie in the interval [tex][0,2\pi)[/tex]

Summarizing. The six solutions are

[tex]x=0,x=\pi,x=\frac{\pi}{3},x=\frac{2\pi}{3},x=\frac{4\pi}{3},x=\frac{5\pi}{3}[/tex]

Answer:

Exact Form: 27/8

Decimal Form: 3.375

Mixed Number Form: 3 3/8

Step-by-step explanation:

3 + 5/8 - 1 + 3/4

I stared by making 5/8 a decimal

which is 0.625

then  added 3 to 0.625 which is 3.625 then subtracted 1 which is 2.625

then i turned 3/4 to a decimal which is 0.75

i added 2.625 and 0.75

which is 3.375

Answer: 0

Step-by-step explanation:

3 and 5 over 8 minus 1 and 3 over 4

= 3 +5/8 - 1+3/4

= 8/8 - 4/4

=1 - 1

=0

Answer:

0.6808

Step-by-step explanation:

First, find the standard deviation of the sample.

s = σ / √n

s = 3 / √49

s = 0.429

Next, find the z-score.

z = (x − μ) / s

z = (28.8 − 29) / 0.429

z = -0.467

Use a calculator or z-score table to find the probability.

Using a table:

P(x > -0.47) = 1 − 0.3192 = 0.6808

Using a calculator:

P(x > -0.467) = 0.6796

The probability that the average mileage of the fleet is greater than 28.8 mpg is approximately 0.680.

Step 1

In order to determine the likelihood that a fleet of 49 automobiles will get more than 28.8 mpg on average, we must apply the Central Limit Theorem, which states that the sample mean's sampling distribution will be roughly normally distributed.

Given:

- Mean [tex](\(\mu\))[/tex]= 29 mpg

- Standard deviation [tex](\(\sigma\))[/tex] = 3 mpg

- Sample size [tex](\(n\))[/tex] = 49 cars

- Sample mean [tex](\(\bar{x}\))[/tex]= 28.8 mpg

Step 2

First, we find the standard error of the mean (SEM):

[tex]\[\text{SEM} = \frac{\sigma}{\sqrt{n}} = \frac{3}{\sqrt{49}} = \frac{3}{7} \approx 0.4286\][/tex]

Next, we convert the sample mean to a z-score to find the probability:

[tex]\[z = \frac{\bar{x} - \mu}{\text{SEM}} = \frac{28.8 - 29}{0.4286} \approx \frac{-0.2}{0.4286} \approx -0.466\][/tex]

We can use a calculator or the conventional normal distribution table to find the probability using the z-score.

With a z-score of -0.466, one may calculate the cumulative probability to be roughly 0.3204. This is the likelihood that the mileage will be on average less than 28.8 mpg.

We deduct this figure from 1 to get the likelihood that the average mileage is higher than 28.8 mpg:

Step 3

[tex]\[P(\bar{x} > 28.8) = 1 - P(\bar{x} < 28.8) = 1 - 0.3204 = 0.6796\][/tex]

Therefore, the probability that the average mileage of the fleet is greater than 28.8 mpg is approximately 0.680 (rounded to three decimal places).

Answer:

x=6/31, y=147/31. (6/31, 147/31).

Step-by-step explanation:

y=-22x+9

y=40x-3

-----------------

-22x+9=40x-3

9=40x-(-22x)-3

9=40x+22x-3

9=62x-3

62x=9+3

62x=12

x=12/62

simplify,

x=6/31

-----------------

y=40(6/31)-3=240/31-3=240/31-93/31=147/31

x=6/31, y=147/31.

Answer:

The length of the side of the square is 6 feet.

Step-by-step explanation:

Given,

Length of side of square = [tex](24 - 3x)\ feet[/tex]

According to question, x = 6

So we have to substitute x with 6 in the given expression.

Length of side of square = [tex](24-3x)= 24-3\times6=24-18=6\ feet[/tex].

Thus the length of the side of the square is 6 feet.

Final answer:

To find the length of the side of the square when x is 6, substitute 6 for x into the given expression (24 - 3x). Thus, the length of the side is calculated as 6 feet.

Explanation:

The student asked for the length of the side of the square when x = 6. To find this, we substitute x with 6 into the expression representing the side length of the square, which is (24 - 3x) feet.

Replacing x with 6, we get:

The length of the side of the square when x is equal to 6 is therefore 6 feet.

Answer:

a.   s = 0.9r

not very sure about b

Step-by-step explanation:

They need to babysit for 10 hours to have same money each day.

Step-by-step explanation:

On Thursday;

Charges = $3 per hour

Initial fee = $40

let x be the number of hours.

T(x) = 3x+40

On Friday;

Charges = $4 per hour

Initial fee = $30

F(x)= 4x+30

The cost will be same when;

T(x) = F(x)

[tex]3x+40=4x+30\\40-30=4x-3x\\10=x\\x=10[/tex]

They need to babysit for 10 hours to have same money each day.

Keywords: functions, addition

Learn more about functions at:

#LearnwithBrainly

Step-by-step explanation:

denominator separately

[tex]277 \sqrt{3} [/tex]

the below 160 Number 2) Same thing with the first one Multiply the Fraquetions, then multiply the numerator and denominator separately so

[tex] \frac{590}{160} \sqrt{17} [/tex]

then change to

[tex]590 \sqrt{17} [/tex]

the below that is a 5 and above it on the top right corner out 160

Answer:

C

[tex]6\sqrt{x} 5-4\sqrt{x} 15[/tex]

Answer:

6√5 - 4√3

Step-by-step explanation:

The question ask us to simplify the square root of 5 times the quantity 6 minus 4 square root of 3 . The word expression can be represented mathematically as follows:

√5 × 6 - 4√3 . The expression forms a Surd.

√5 × 6 - 4√3

6√5 - 4√3

Answer:

$2853.5

Step-by-step explanation:

Let us assume that the interest rate of both the investments of Haley is simple interest.

So, $16820 amounts of investment in nine-year CD bearing 5.8% interest will get interest of [tex]16820 \times \frac{5.8}{100} \times 9 = 8780[/tex] dollars.

Again, $21950 amounts of investment in an online savings account giving 3% interest will give interest of [tex]21950 \times \frac{3}{100} \times 9 = 5926.5[/tex] dollars.

Therefore, the nine-year CD will give more interest by $(8780 - 5926.5) = $2853.5. (Answer)

Answer:

C. $2,853.54

Step-by-step explanation:

I just answered it correct

Answer:

A=(5/2x+10)(5/2x+5)

Step-by-step explanation:

A=LW

A=(5/2x+10)(5/2x+5)

Answer:

The temperature at noon is 6ºF.

Step-by-step explanation:

3:00am: -10ºF

               -12ºF

6:00am: -22ºF

              +8ºF

9:00am: -14ºF

              +20ºF

Noon:     6ºF

So at 6:00 a.m. the temperature is 33 F

12:00 p.m. the temperature increased by 10 F so it is 43 F

3:00 p.m. the temperature increased by another 12 F making it 55 F

At 10:00 p.m. it would decrease by 15 F making it 40 F.

The temperature would need to fall/decrease 7 F to reach the original temperature of 33 F so it would be A.

Hope this helps!

Can u plz mark me as brainliest? I really need it!

Answer: 24 people are in the class

I am sorry I don’t know the equation but I hope this helps.

Step-by-step explanation:

3. 18. 18

- =. —. =. —-

4. ? 24

The molar mass of dinitrogen monoxide?

Is=N2O=(14×2)+16

=44g/mol

Final answer:

The molar mass of dinitrogen monoxide (N₂O) is 44.02 g/mol, calculated by adding the atomic masses of two nitrogen atoms (14.01 g/mol each) and one oxygen atom (16.00 g/mol).

Explanation:

The molar mass of dinitrogen monoxide, which is chemically denoted as N₂O, can be calculated by adding together the atomic mass of nitrogen with the atomic mass of oxygen. Nitrogen (N) has an atomic mass of approximately 14.01 g/mol, and since we have two nitrogen atoms, we multiply this by 2. Oxygen (O) has an atomic mass of about 16.00 g/mol. Therefore, the molar mass of dinitrogen monoxide is:

(14.01 g/mol × 2) + (16.00 g/mol × 1) = 28.02 g/mol + 16.00 g/mol = 44.02 g/mol.

This value represents the weight of one mole of dinitrogen monoxide molecules. The importance of knowing the molar mass of a compound like dinitrogen monoxide relates to the calculations involved in chemical reactions and stoichiometry, specifically when dealing with gases under various conditions of temperature and pressure.

Answer: The answer is B.

Step-by-step explanation:

Final answer:

The correct transformation that carries the figure onto itself is Option B: reflecting across the line y=1 and rotating 1080° clockwise about the point (-7,1), as the 1080° rotation is a multiple of 360° and does not change the figure's orientation.

Explanation:

The question is asking to identify the transformation that can be applied to a figure such that the figure maps onto itself. We're given various options that involve a reflection and a rotation. Reflection across a line like y=1 would flip the figure over this horizontal line. A rotation of 1080° clockwise about a point is equivalent to a full 360° rotation three times (since 1080° = 360° × 3), which would bring the figure back to its original position, effectively leaving it unchanged.

The correct answer is Option B, which includes a reflection across the line y=1 and a 1080° clockwise rotation about the point (-7,1). This is because the 1080° rotation, being an integer multiple of full circles, results in no net rotation, so the figure looks exactly the same after this operation. The reflection flips the figure across the line y=1 but, when combined with the rotation, it results in the figure mapping onto itself.

Options A and C suggest a 990° rotation, which is not a multiple of 360° and therefore would not result in the figure mapping onto itself. Option D suggests reflecting across the line x=-6, which is not in the given options for the reflection, and a 1080° rotation about the point (-7,1), which would rotate the figure back onto itself after the reflection, but the reflection line is incorrect.

Answer:

-1/10

Step-by-step explanation:

1/2 - 3/5

Find common denominator. in this case, it'll be 10

1/2 * 5/5 = 5/10

3/5 * 2/2 = 6/10

5/10 - 6/10 = -1/10

Answer:

The answer is 24/2=36/3=66/5.5=108/9=180/15.

Step-by-step explanation:

Given:

24/2=_/3=_/5.5=108/_=_/15.

Now, we need to solve this by putting [tex]x[/tex] in the place of _ and then continue:

[tex]\frac{24}{2} =\frac{x}{3}[/tex]

By cross multiplication we get:

[tex]72=2x[/tex]

By dividing with 2 we get:

[tex]36=x[/tex]

Now, we will continue like this process:

[tex]\frac{36}{3}=\frac{x}{5.5}[/tex]

[tex]198=3x[/tex]

[tex]x=66[/tex]

And, then again:

[tex]\frac{66}{5.5}=\frac{108}{x}[/tex]

[tex]66x=594[/tex]

[tex]x=9[/tex]

And, last:

[tex]\frac{108}{9}=\frac{x}{15}[/tex]

[tex]9x=1620[/tex]

[tex]x=180[/tex]

Therefore, the answer is 24/2=36/3=66/5.5=108/9=180/15.

Answer:

The range of g(x) =  {-11,-9,-7,-5}.

Step-by-step explanation:

Given:

g(x) = x – 13 over the domain {2, 4, 6, 8).

Now, to evaluate:

Putting [tex]x=2[/tex]

[tex]g(2)=2-13=-11[/tex]

Putting [tex]x=4[/tex]

[tex]g(4)=4-13=-9[/tex]

Putting[tex]x=6[/tex]

[tex]g(6)=6-13=-7[/tex]

Putting [tex]x=8[/tex]

[tex]g(8)=8-13=-5[/tex]

So, the range is {-11,-9,-7,-5}.

Therefore, the range of g(x) =  {-11,-9,-7,-5}.

Answer:

-0.37

Step-by-step explanation:

Answer:

Part a) [tex]6x+4y=48[/tex]

Part b) The graph in the attached figure

Part c) (6,3) and (4,6)

Step-by-step explanation:

Part a) Write a linear equation to represent the number of items you can buy if she spends $48

Let

x ----> number of package of cupcakes you can buy

y ---> number of package of cookies you can buy

we know that

The number of package of cupcakes you can buy multiplied by it cost ($6 for a package) plus the number of package of cookies you can buy multiplied by it cost ($4 for a package) must be equal to $48

so

The linear equation that represent this problem is

[tex]6x+4y=48[/tex]

Part b) Graph the equation

To graph the line we need two points

Find the intercepts

Find the x-intercept (value of x when the value of y is equal to zero)

For y=0

[tex]6x+4(0)=48[/tex] ----> [tex]x=8[/tex]

the x-intercept is the point (8,0)

Find the y-intercept (value of y when the value of x is equal to zero)

For x=0

[tex]6(0)+4y=48[/tex] ----> [tex]y=12[/tex]

the y-intercept is the point (0,12)

Plot the intercepts and join the points to graph the line

see the attached figure

Part c) State two possible solutions in the context of the problem

1) First possible solution

the ordered pair (6,3)

That means

You can buy 6 package of cupcakes and 3 package of cookies

Verify in the linear equation

[tex]6(6)+4(3)=48[/tex]

[tex]48=48[/tex] ---> is true

therefore

The ordered pair is a solution of the linear equation

2) Second possible solution

the ordered pair (4,6)

That means

You can buy 4 package of cupcakes and 6 package of cookies

Verify in the linear equation

[tex]6(4)+4(6)=48[/tex]

[tex]48=48[/tex] ---> is true

therefore

The ordered pair is a solution of the linear equation

Answer:

D

Step-by-step explanation:

Firstly, perpendicular line has a slope that is "negative reciprocal" of the given line's slope.

The equation of a line is  y = mx + b

Where m is the slope and b is the y-intercept

So, the given line has a slope of "-4", hence the perpendicular line would have a slope of "1/4". So immediately we can eliminate Answer Choice "A".

Now, let's see which of the other choices is our correct answer. Since we know this line has slope of "1/4", we can write:

y = (1/4)x + b

Given the point (4,5), we can replace "x" with "4" and "y" with 5 and find b:

[tex]y=\frac{1}{4}x+b\\5=\frac{1}{4}(4)+b\\5=1+b\\b=5-1\\b=4[/tex]

So, the equation is:

[tex]y=\frac{1}{4}x+4[/tex]

Correct answer is D