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.)

i) Michaelangelo's sells small, medium, large, and jumbo pizzas. - Not nominal data.

Nominal data refers to a type of categorical data where values are assigned to distinct categories or labels without any inherent order or numerical significance. In the given options, both i) and ii) involve categorical information, but only option ii) ("Michaelangelo's most-requested toppings are pepperoni, black olives, and mushrooms") describes nominal data.

In option i), the sizes of pizzas (small, medium, large, and jumbo) can be considered ordinal data as they have a specific order and imply a relative size difference. Ordinal data possesses a sequential arrangement where the categories have a meaningful relationship or hierarchy.

On the other hand, option ii) presents toppings (pepperoni, black olives, and mushrooms) as distinct categories without any inherent order or hierarchy.

Each topping represents a separate label or category, making it an example of nominal data.Therefore, option ii) ("Michaelangelo's most-requested toppings are pepperoni, black olives, and mushrooms") accurately describes nominal data.

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Answer:

Scale factor is 3/5

Step-by-step explanation:

Compare corresponding parts of one triangle to corresponding parts of other

9/15 = 3/5

scale factor is 3/5

Answer:

II and III

Step-by-step explanation:

Parallel lines have the same gradient, they will have the same coefficient in front of x

II: 2x + 3y = 6 needs to be rearranged to 3y = -2x + 6 and then y = -2/3x + 2: the gradient is -2/3

III: y - 8 = -2/3(x - 3) needs to expanded so y - 8 = -2/3x + 2 and then y = -2/3x + 10: again, the gradient is -2/3

The two lines are parallel because both gradients are -2/3

Hope this helps!

Compared with income-based repayment plans, the standard repayment plan will generally  Minimize the amount of interest paid.

Income-driven repayment plans give installment options for numerous government student credit borrowers that bring down their monthly installment amount. if you enlist in an Income-Driven Repayment arrangement, your month-to-month payment is based on your salary and family size and not totally on how much you owe. The month-to-month installment on income-driven repayment plans will be lower than the standard repayment plan. The installment may indeed be zero for borrowers with low or no income. The lower loan installments may make income-driven repayment plans a great choice for borrowers who are battling to reimburse their student loans. However, indeed in spite of the fact that the remaining debt is excused after 20 or 25 a long time of repayment, the credit forgiveness may be taxable.

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The final simplified expression is: -211/7i - 3/7

To simplify the given expression, let's work step by step:

(4 - i)(-3/7i) - 7i(8/2i)

First, let's simplify each multiplication:

(4 * -3/7i - i * -3/7i) - (7i * 8/2i)

Now, simplify further:

(-12/7i + 3/7i^2) - (56/2)

Remember that i^2 is equal to -1:

(-12/7i + 3/7(-1)) - (28)

Simplify the expression:

(-12/7i - 3/7) - 28

Combining like terms:

-12/7i - 3/7 - 28

Now, let's express the terms as a single fraction:

-12/7i - 3/7 - 196/7

Combine the numerators:

(-12 - 3 - 196)/7i - 3/7

Simplify further:

(-211)/7i - 3/7

The final simplified expression is:

-211/7i - 3/7

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First expand the equation.

-5e+5+6e = -17

Next, combine the like terms.

e+5 = -17

e = -22

The remaining two angles of the given isosceles triangle is Option(C) 40°,70° .

For an isosceles triangle, the two sides of the triangle are congruent and equal in length . Also the angles subtending the adjacent equal sides of the isosceles triangle are of same measure.  

We also know that the sum of the three interior angles of any triangle is always equal to 180° .

In the options given, in Option(C) the angles measure 40° and 70° .

Thus as one angle of the isosceles triangle is given to be 70°, the other angle of its adjacent side is also 70° .

The sum of the interior angles of the triangle is equal to -

70° + 40° + 70° = 180° which satisfies the property.

Therefore, the remaining two angles of the given isosceles triangle is Option(C) 40°,70° .

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Answer:$509.51

Step-by-step explanation:

The volume of a right cylinder is given by:

V = πr^2h

where r is the radius and h is the height.

Plugging in the values given in the problem, we get:

V = π(0.5)^2(25) = 19.63 cubic feet

The cost of the utility pole is the product of its volume and the cost per cubic foot of the wood, which is $25.99. Therefore, the cost is:

Cost = 19.63 x $25.99 = $509.51

Rounding to the nearest cent, the cost of the utility pole is $509.51.

The correct answer is d. 56.

When computing a correlation coefficient, the degrees of freedom (df) is calculated as (n-2), where n is the sample size. In this case, we are given that df = 55.

Substituting df = 55 into the formula, we get:

55 = n - 2

Adding 2 to both sides, we get:

n = 57

Therefore, the sample size must be 57 in order to have 55 degrees of freedom when computing a correlation coefficient.
Hi! When computing a correlation coefficient with 55 degrees of freedom, your sample size must be 57 (Option c).

Here's the step-by-step explanation:
1. Recall that the formula to find degrees of freedom (df) in correlation is df = n - 2, where n is the sample size.
2. In this case, the degrees of freedom is given as 55.
3. To find the sample size (n), you'll need to rearrange the formula: n = df + 2.
4. Substitute the given degrees of freedom into the formula: n = 55 + 2.
5. Solve for n: n = 57.

Therefore, when computing a correlation coefficient with 55 degrees of freedom, your sample size must be 57.

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Answer:

Step-by-step explanation:

Your difference of perfect cubes formula is given as

\((a-b)(a^2+ab+b^2)\) and you have already correctly identified a as \(5q^2\)  and b as \(r^2s\). So we fill in the formula as follows:

\((5q^2-r^2s)((5q^2)^2+(5q^2)(r^2s)+(r^2s)^2)\) and we simplify.  Remember that

\((5q^2)^2=(5)^2*(q^2)^2=25q^4\). It's important that you remember the rules.

Simplifying then gives us

\((5q^2-r^2s)(25q^4+5q^2r^2s+r^4s^2)\)

That's it, so fill it in however you need to on your end. Learn the patterns for the sum and difference of cubes and it will save you a ton of headaches...promise!!

Answer: If each of the s swimmers on the relay team swam an equal number of the 8 laps in a race, the expression that shows how many laps each swimmer swam would be 8/s.

This expression shows that each swimmer swam 8 laps, divided by the total number of swimmers on the team, s.

So, if there are 's' swimmers on the relay team, each swimmer swam 8/s laps.

Step-by-step explanation:

According the given question the value οf x is (b+1)/(d-a).

Tο simplify simply means tο make anything easier. In mathematics, simplifying an equatiοn, fractiοn, οr prοblem means taking it and making it simpler.

Calculatiοns and prοblem-sοlving techniques simplify the issue. Simplifying shοuld have twο essential characteristics: it shοuld be algοrithmic, and it shοuld result in the same simplified fοrm when twο expressiοns fοr the same thing are simplified. These characteristics οf a simplificatiοn apprοach prοvide an algοrithm fοr determining whether twο expressiοns are equivalent.

Here, we have

Given: ax+b=dx-1,  if a≠d

We have tο find the value οf x.

We apply simplificatiοn here and we get

ax+b = dx-1

b + 1 = dx - ax

b +1 = x(d-a)

x = (b+1)/(d-a)

Hence, the value οf x is (b+1)/(d-a).

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A. The correlation coefficient (r) is given as 29.4%. To find r, divide by 100: r = 0.294. This indicates a positive, but weak, correlation between drop height and duration for the 90 roller coasters.

B. The coefficient of determination (R^2) is the square of the correlation coefficient (r). Calculate R^2 = (0.294)^2 ≈ 0.086. This means that approximately 8.6% of the variation in ride duration can be explained by the variation in drop height.

C. For the Tower of Terror, the regression model may not provide an accurate prediction of ride duration based on its drop height, as it is an outlier with a large drop but a short ride duration. The weak correlation between drop height and duration for the remaining 90 coasters suggests that this model may not be a good predictor for unusual cases like the Tower of Terror.

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Answer:

69 INCHES

Step-by-step explanation:

Given that :

Height of father's eye above the flat ground :

Kindly check attached picture for diagram:

To obtain the value of h ; we can use Pythagoras rule ;

Tan θ = opposite / Adjacent

Tan 48 = h / 15

15 tan 48 = h

37.126302 = h

h = 37.

Hence, height of father's above the flat ground :

h + 32 = 37 + 32= 69 inches

Answer:

\(c^2 = 9dp\)

Step-by-step explanation:

Given

\(dx^2 + cx + p = 0\)

Let the roots be \(\alpha\) and \(\beta\)

So:

\(\alpha = 2\beta\)

Required

Determine the relationship between d, c and p

\(dx^2 + cx + p = 0\)

Divide through by d

\(\frac{dx^2}{d} + \frac{cx}{d} + \frac{p}{d} = 0\)

\(x^2 + \frac{c}{d}x + \frac{p}{d} = 0\)

A quadratic equation has the form:

\(x^2 - (\alpha + \beta)x + \alpha \beta = 0\)

So:

\(x^2 - (2\beta+ \beta)x + \beta*\beta = 0\)

\(x^2 - (3\beta)x + \beta^2 = 0\)

So, we have:

\(\frac{c}{d} = -3\beta\) -- (1)

and

\(\frac{p}{d} = \beta^2\) -- (2)

Make \(\beta\) the subject in (1)

\(\frac{c}{d} = -3\beta\)

\(\beta = -\frac{c}{3d}\)

Substitute \(\beta = -\frac{c}{3d}\) in (2)

\(\frac{p}{d} = (-\frac{c}{3d})^2\)

\(\frac{p}{d} = \frac{c^2}{9d^2}\)

Multiply both sides by d

\(d * \frac{p}{d} = \frac{c^2}{9d^2}*d\)

\(p = \frac{c^2}{9d}\)

Cross Multiply

\(9dp = c^2\)

or

\(c^2 = 9dp\)

Hence, the relationship between d, c and p is: \(c^2 = 9dp\)

Answer:

238

Step-by-step explanation:

the quotient simply means the result of the division. when you divide 952 by 4, you get 238

If we assume that point C is somewhere on segment AD, then,

AD = AC + CD

AD = (9x-12) + (4x+18)

AD = (9x+4x) + (-12+18)

AD = 13x+6    is the answer

b) To make a conclusion, you need to calculate the confidence interval using the sample mean, the sample size, and the appropriate t or z-score corresponding to your desired confidence level. Then you can compare the confidence interval with the desired percentage range to assess if it is likely that the population mean falls within that range.

To determine the minimum sample size required to construct a confidence interval for the population mean with a given margin of error, we can use the following formula:

n = (Z * σ / E)^2

Where:

n is the required sample size,

Z is the z-score corresponding to the desired confidence level (expressed as a decimal),

σ is the population standard deviation, and

E is the desired margin of error.

(a) Let's assume that the desired confidence level is represented by % (e.g., 95%, 99%), and the margin of error is expressed in milligrams. Without specific values provided for the confidence level or margin of error, we can't calculate the minimum sample size precisely. However, using the formula mentioned above, you can plug in the appropriate values to determine the minimum sample size based on your desired confidence level and margin of error.

(b) To determine if the population mean could be within a certain percentage of the sample mean, we need to consider the margin of error and the confidence interval. The margin of error represents the range within which the population mean is likely to fall based on the sample mean.

If the population mean is within the margin of error of the sample mean, it suggests that the population mean could indeed be within that percentage range of the sample mean. However, without specific values provided for the margin of error or the confidence interval, we can't determine if the population mean is likely to be within a certain percentage of the sample mean.

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1. The outcomes in the sample space of choosing a letter from the word STARK are: S, T, A, R, K.

2. Number of outcomes in the sample space = 6 (from THANKS) × 5 (from STARK) = 30.

3. The Probability of choosing the letters AA is 0, as there are no occurrences of the letter A in both words together.

1. The outcomes in the sample space of choosing a letter from the word THANKS are: T, H, A, N, K, S.

  The outcomes in the sample space of choosing a letter from the word STARK are: S, T, A, R, K.

2. To find the number of outcomes in the sample space, we multiply the number of outcomes for each word.

  Number of outcomes in the sample space = Number of outcomes for the first word × Number of outcomes for the second word

  Number of outcomes in the sample space = 6 (from THANKS) × 5 (from STARK) = 30.

3. The probability of choosing the letters AA would be the number of favorable outcomes (which is 0 in this case) divided by the total number of outcomes in the sample space.

  Probability of choosing AA = Number of favorable outcomes / Total number of outcomes

  Probability of choosing AA = 0 / 30 = 0.

Therefore, the probability of choosing the letters AA is 0, as there are no occurrences of the letter A in both words together.

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Answer:

$175.83

Step-by-step explanation:

All you have to do is 4220 divided by 24 = $175.83

Answer:

Sorry that me lines are bad :(

Step-by-step explanation:

Hope this helps ;) ;p

Answer: y=18, x=30

Step-by-step explanation:

The total weight of the liquid in the tank is approximately 16,425 pounds if the tank is in the shape of a hemisphere and has a radius of 5 feet.

Radius of tank = 5 feet

Density = 62.7 pounds per cubic foot

The hemisphere's volume is calculated by using the formula:

\(V = (2/3)*(3.14)r^3\)

V = \((2/3)* (3.41)*(5 ft)^3\)

V = 261.8 ft cubic centimeter.

The weight of the liquid is calculated by multiplying volume and density:

W = V × D

W = \(261.8 ft^3 * 62.7 lb/ft^3\)

W = 16425.2 lbs.

Therefore we can conclude that the total weight of the liquid in the tank is approximately 16,425 pounds.

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Answer:

218

Step-by-step explanation:  

ATQ,

22%of total books = 48

Let the total no. of books in library be x.

22/100x=48

x=4800/22

X=218(approximately)

Answer:

The correct graph should have x values that have no more than one y value.

Step-by-step explanation:

A the inputs (x values) of a function can have no more than one y value. This is a "fact" for functions. So you should click on the graph until you see a graph where every x value has exactly 0 or 1 y value.

Substituting x = 1, we get:

y''(1) = 16/√3.

To solve the differential equation (y^(1/3)x)dy/dx = 1/x, we need to separate the variables and integrate both sides with respect to their respective variables.

First, we can rewrite the equation as:

dy/y^(1/3) = (dx/x)

Next, we can integrate both sides:

∫dy/y^(1/3) = ∫dx/x

Integrating the left side, we use the substitution u = y^(1/3), du = (1/3)y^(-2/3)dy:

3∫du/u = ln|u| + C1 = ln|y^(1/3)| + C1

Integrating the right side, we get:

∫dx/x = ln|x| + C2

Putting the two integrals together, we have:

ln|y^(1/3)| = ln|x| + C

where C = C2 - C1

To solve for y, we can exponentiate both sides:

|y^(1/3)| = e^C|x|

Since y(1) = 4, we can use this initial condition to solve for the constant C:

|4^(1/3)| = e^C|1|

C = ln(4^(1/3)) = ln(2/√3)

Substituting C into the equation above, we get:

|y^(1/3)| = e^(ln(2/√3))|x| = (2/√3)|x|

Squaring both sides and solving for y, we get:

y = (2/√3)^3x^3 = (8/3√3)x^3

Finally, to express y''(1) in terms of x, we take the second derivative of y:

y = (8/3√3)x^3

y' = 8x^2/√3

y'' = 16x/√3

Substituting x = 1, we get:

y''(1) = 16/√3.

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Answer:

x < 2

Step-by-step explanation:

The indicated part is left from point 2.

You see an open circle at point (2,0) which means you should exclude the point x = 2 in the inequation.

Now you have enough info to get the right inequality:

x < 2