Whats the geometric mean of 6 and 9

The rectangular prism is 3 inches by 4.75 inches by 20.5 inches, has a total surface area of 346.25 in².

We need to find the surface area of an object, the surface area of a solid three-dimensional object is the area of the boundary surface of the object and its surroundings, therefore:

The dimensions of the rectangular prism will be as follows:

Let the length of the rectangular prism = 3 inches

Let the width of the prism = 4.75 inches

Let the height of the prism = 20.5 inches

Therefore, the surface area, A, of a rectangular prism can be found using the formula:

A = 2 × Length × Width + 2 × Length × Height + 2 × Height × Width

Therefore, the surface area of the rectangular prism in the question is found as follows:

Area, A = 2 × 3 × 4.75 + 2 × 3 × 20.5 + 2 × 20.5 × 4.75 = 346.25

The total surface area of the rectangular prism is 346.25 in².

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Answer:

346.25

Step-by-step explanation:

took the test :)

Answer:

to be safe

Step-by-step explanation:

the further you are the better, because we don't know who have the virus from who don't have it it's better to be 6 feet apart frome each other where ever you go.

Answer:

84° and 48°

Step-by-step explanation:

1st of all, the inner angle of rhombus would total up into 360° and the opposite for each angle is equal to each other.

As ∆WXY = 84°, so

∆WZY = 84°

Any diagonal line in the rhombus would make the angle get divided equally i.e ∆XWZ

So find ∆XWZ first.

∆XWZ = (360° - 84° - 84°) ÷ 2

= 192° ÷ 2

= 96°

∆XWY = 96° ÷ 2

= 48°

Answer:

3. The mean will increase more than median, but both will increase.

Step-by-step explanation:

We have been given a dot plot. We are asked to find the true statement, if a new data point at 12 is added to our given dot plot.

Since we know that an large valued outlier affects mean more than median, so mean will increase more than median.

Let us check this using our given information. Our data set before adding 12 is:

1, 2, 2, 2, 3, 4, 4, 4, 5.

We can see that our data set has odd number (9) of data points, so median will be the value of 5th term, that is 3.

Therefore, mean of our data set is 3.

Upon adding a data point at 12, our new data set will be:

1, 2, 2, 2, 3, 4, 4, 4, 5, 12.

Now our data set has 10 terms, so median will be the average of 5th and 6th term.

Therefore, the median of new data set will be 3.5.

Therefore, mean of new data set will be 3.9.

Upon looking at our given statements we can see that 3rd statement is true as mean and median both increased after adding 12 to our data set, but mean increased more that median. Mean and median before adding 12 was 3; but after adding 12 median became 3.5, while mean became 3.9 (which is greater than mean).

Step-by-step explanation:

Based on the definition of an isosceles trapezoid, the measure of angle MQP in the figure shown is: m∠MQP = 73°.

An isosceles trapezoid has the following properties:

The figure given is an isosceles trapezoid.

The measure of angle MNP is given as 107°.

Angle MQP and angle MNP are opposite angles.

Based on the properties of an isosceles trapezoid, we have:

m∠MQP + m∠MNP = 180

Substitute

m∠MQP + 107 = 180

m∠MQP = 180 - 107

m∠MQP = 73°

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Answer:

t is a: Transversal

<1 and <7 are: Exterior Angles

<2 and<6 are: Corresponding Angles

<4 and <5 are: Alternate Interior Angles

a and b are: Parallel Lines

<4 and <6 are: Consecutive Interior Angles

<2 and <7 are: Alternate Exterior Angles

<5 and <6 are: Interior Angles

I hope this helps!

The answers are =

a) the number of different anagrams possible is 181,440.

b) the number of anagrams that satisfy the conditions is 181,439.

(a) The number of different anagrams (including the trivial arrangement) of the word "VIKINGS" can be calculated using the formula for permutations of a multiset.

Since "VIKINGS" has repeated letters (2 "I"s), we need to divide the total number of permutations by the factorial of the number of repetitions.

The expression to calculate the number of anagrams is:

10! / (2! × 1! × 1! × 1! × 1! × 1! × 1!)

Simplifying this expression, we get:

10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 / (2 × 1 × 1 × 1 × 1 × 1 × 1 × 1 × 1 × 1)

This evaluates to:

362,880 / 2

So, the number of different anagrams possible is 181,440.

(b) To calculate the number of anagrams where the two "L"s are consecutive, we can treat them as a single unit. So, we have the word "VIKINGSLL".

Now, we can treat the "VIKINGSLL" as a single entity and calculate the number of permutations of these 9 elements.

However, we need to consider that the two "L"s within the "LL" unit can also be rearranged.

The expression to calculate the number of anagrams with the two "L"s next to each other is:

9! / (2! × 1! × 1! × 1! × 1! × 1! × 1! × 1! × 1!)

Simplifying this expression, we get:

9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 / (2 × 1 × 1 × 1 × 1 × 1 × 1 × 1 × 1)

This evaluates to:

362,880 / 2

Hence, the number of anagrams with the two "L"s next to each other is 181,440.

To calculate the number of anagrams that satisfy the condition that "V" cannot be first and "S" cannot be last, we subtract the number of anagrams that don't satisfy this requirement from the total number of anagrams (181,440):

181,440 - 1

So, the number of anagrams that satisfy the conditions is 181,439.

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Sylvia and Patrick gathered information on the weight of cars and the mileage they get, and then proceeded to plot the data on a graph.

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The rewritten form of the given expression such that it is without absolute value notation is; 2b.

It follows from the task content that the rewritten form of the given expression; | 2b | is to be determined.

On this note, since it is given that the variable b is less than zero; i.e b < 0.

It follows that the expression evaluation of 2b yields a negative number.

However, the rewritten form of the expression without the absolute value notation since the value of b is unknown still remains; 2b.

Therefore, the required rewritten form is; 2b.

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the company uses 37 screws to make each table and 14 screws to make each chair. The company needs to order screws for 12 tables and 48

Answer:

x^2+2x-15

Step-by-step explanation:

x^2+5x-3x-15

=x^2+2x-15

Answer:

x² + 2x -15

Step-by-step explanation:

by using FOIL method (see attached for reference),

(x-3)(x+5)

= (x)(x) + (x)(5) + (-3)(x) + (-3)(5)

= x² + 5x - 3x -15

= x² + 2x -15

volume : 7.5 cm²

\(\hookrightarrow \sf Length \ * Width \ * \ Height\)

\(\hookrightarrow \sf 2 \ * 1\dfrac{1}{4} \ * \ 3\)

\(\hookrightarrow \sf 2 \ * \dfrac{5}{4} \ * \ 3\)

\(\hookrightarrow \sf \dfrac{15}{2}\)

\(\hookrightarrow \sf 7.5 \ cm^2\)

Answer:

\(\sf volume=7 \frac12 \ cm^3\)

Step-by-step explanation:

Formula

volume of cuboid = length × width × height

Given dimensions of the ice cube:

Substituting the given values into the formula:

\(\sf \implies volume=2\times 1 \frac14 \times 3\)

Converting to improper fractions:

\(\sf \implies volume=\dfrac21\times \dfrac54 \times \dfrac31\)

                  \(\sf =\dfrac{ 2\times 5 \times 3}{1 \times 4 \times 1}\)

                  \(\sf =\dfrac{30}{4}\)

Dividing the numerator and denominator by the highest common factor:

\(\sf \implies volume=\dfrac{30 \div 2}{4 \div 2}\)

                  \(\sf =\dfrac{15}{2}\)

Converting the improper fraction into a mixed number:

\(\sf \implies volume=7 \frac12 \ cm^3\)

The slope of the regression line is 0.0138. - If the depth of the dive is increased by one meter, it adds 0.0138 minutes to the time spent underwater. (Correct) - If the depth of the dive is decreased by one meter, it subtracts 0.0138 minutes from the time spent underwater. (Incorrect) - If the depth of the dive is increased by 0.0138 meter, it adds approximately 0.001 minute (or 0.06 seconds) to the time spent underwater. (Incorrect)

Step 1:

The slope of the regression line is 0.0138.

Step 2:

The slope of 0.0138 in this context indicates that for every additional meter in depth, the penguin spends an additional 0.0138 minutes (or approximately 0.83 seconds) underwater. In other words, as the penguin dives deeper, it tends to stay underwater for a slightly longer duration.

To address the provided options:

- The first option, "If the depth of the dive is increased by one meter, it adds 0.0138 minutes to the time spent underwater," is correct based on the given slope value. Increasing the depth by one meter corresponds to adding 0.0138 minutes to the dive duration.

- The second option, "If the depth of the dive is decreased by one meter, it adds 0.0138 minutes to the time spent underwater," is incorrect. According to the slope, decreasing the depth by one meter would actually result in a decrease of 0.0138 minutes in the dive duration.

- The third option, "If the depth of the dive is increased by 0.0138 meter, it adds one minute to the time spent underwater," is incorrect. The slope indicates that for an increase of 0.0138 minutes (or approximately 0.83 seconds) in dive duration, the depth would need to increase by one meter.

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The complete question is:

A study of king penguins looked for a relationship between how deep the penguins dive to seek food and how long they stay underwater. For all but the shallowest dives, there is a linear relationship that is different for different penguins. The study report gives a scatterplot for one penguin titled The relation of dive duration (DD) to depth (D). Duration DD is measured in minutes and depth D is in meters. The report then says, The regression equation for this bird is: DD = 2.69 + 0.0138D.

Step 1:

What is the slope of the regression line?

Step 2:

Explain in speci?c language what this slope says about this penguin's dives.

If the depth of the dive is increased by one meter, it adds 0.0138 minutes to the time spent under water.

If the depth of the dive is decreased by one meter, it adds 0.0138 minutes to the time spent under water.

If the depth of the dive is increased by 0.0138 meter, it adds one minute to the time spent under water.

Answer:

1200

Step-by-step explanation:

i=prt is the interest equation however we must find the total because it says After 2 years

first lets do 1000*.1*2=200

1000+200=

1200

Answer:

-16

Step-by-step explanation:

g(x) = (x + 5)2 - 12

g(-7)=(-7+5)2-12

g(-7)=(-2)2-12

g(-7)=-4-12

g(-7)=-16

Therefore, option (c)normality assumption is checked when looking at a  Q–Q plot in one-way ANOVA model.

In statistics, a Q–Q plot is a probability plot, a graphical method for comparing two probability distributions by plotting their quantiles against each other. A point on the plot corresponds to one of the quantiles of the second distribution plotted against the same quantile of the first distribution

Here,

normality assumption is checked when looking at a Q–Q plot in one-way ANOVA model.

Explanation: The core tenet of the assumption of normality states that the sample mean distribution (across independent variables) is normal. Technically speaking, the Assumption of Normality asserts that the mean's sampling distribution or the distribution of means among samples is normal.

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The triangle represents delta notation change in y over change in x. the correct option is C.

The pace at which one quantity changes in relation to another quantity is known as the rate of change function. Simply said, the rate of change is calculated by dividing the amount of change in one item by the equal amount of change in another.

The average rate of change is calculated by the formula,

Rate of change = Δy / Δx

Here, the triangle represents the rate of change of the y coordinate with respect to the rate of change of the x coordinate.

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Answer:

Step-by-step explanation:

The general form of this equation is

\(A=Pe^{rt}\) where P is the initial population, e is Euler's number (a constant), r is the rate of decay, and t is the time in years.

Therefore, filling in:

\(A=45000e^{-.02t\)

The absolute value of the elasticity coefficient for Toasty Hands' gloves is 394,265.23.

The elasticity coefficient is calculated as follows:

Elasticity coefficient = (Change in demand)/(Change in price) * (Original price)/(Original demand)

In this case, the change in demand is 540,000 - 440,000 = 100,000 pairs. The change in price is 239 - 279 = -40. The original price is $279, and the original demand is 440,000 pairs.

Plugging these values into the formula, we get:

Elasticity coefficient = (100,000)/(-40) * (279)/(440,000) = -394,265.23

The absolute value of the elasticity coefficient is 394,265.23. This means that the demand for Toasty Hands' gloves is elastic, meaning that a small change in price will lead to a large change in demand.

Here is a more detailed explanation of the calculation:

The change in demand is calculated by subtracting the original demand from the new demand. In this case, the new demand is 540,000 pairs, and the original demand is 440,000 pairs. So the change in demand is 540,000 - 440,000 = 100,000 pairs.

The change in price is calculated by subtracting the original price from the new price. In this case, the new price is $239, and the original price is $279. So the change in price is 239 - 279 = -40.

The original price is $279, and the original demand is 440,000 pairs.

Plugging these values into the formula, we get the elasticity coefficient of -394,265.23.

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The probability that exactly four people get the right letter is 1/120.

Let the people form a line and the envelopes are on the table.

The first person has a 1 in 5 chance of selecting the right letter.  (He selects the correct one)

Now there are 4 on the table so the second person has a 1 in 4 chance of getting the right one (He selects the correct one)

Now there are 3 on the table so the second person has a 1 in 3 chance of getting the right one (He selects the correct one)

Now there are 2 on the table so the second person has a 1 in 2 chance of getting the right one (He selects the correct one)

and so on

so

P(everyone getting the correct letter) = 1/5*1/4*1/3*1/2*1/1=1/5!=1/120.

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Answer:

I hope the image helps!

The 12 ounce can of Coke is the better buy, as it costs $0.50 compared to the $1.00 for the 20 ounce bottle of Pepsi.

When comparing the cost per ounce, the 12 ounce can of Coke costs approximately $0.04 per ounce ($0.50/12), while the 20 ounce bottle of Pepsi costs $0.05 per ounce ($1.00/20). Therefore, the Coke offers a lower cost per ounce, making it the more economical choice. Additionally, if we consider the volume, the 12 ounce can of Coke provides less soda compared to the 20 ounce bottle of Pepsi, meaning you would get more soda for your money with the Pepsi. However, if the goal is to minimize the cost per ounce, the 12 ounce can of Coke is the better buy.

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We need to find the function f(n) whose terms are the same as the series in question. We can then integrate this function from n=1 to infinity and determine if the integral is convergent or divergent. If it is convergent, then the series is convergent. If it is divergent, then the series is also divergent.

To determine whether a series is convergent or divergent using the integral test, we need to first check if the series satisfies three conditions:

1) The terms of the series are positive.

2) The terms of the series are decreasing.

3) The series has an infinite number of terms.

Assuming these conditions are satisfied, we can use the integral test which states that if the integral of the function f(x) from n=1 to infinity is convergent, then the series with terms a_n = f(n) is also convergent. Conversely, if the integral is divergent, then the series is also divergent.

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Answer: 3x

Step-by-step explanation:

Answer:

The dotted line is 4.9

Step-by-step explanation:

The lower triangle is a right triangle so we can use the Pythagorean theorem

a^2+b^2 = c^2

where a and b are the legs and c is the hypotenuse

2^2 + 4^2 = c^2

4+16 = c^2

20 =c^2

Taking the square root of each side

sqrt(20) = c

The upper rectangle has a length of sqrt(20) and a height of 2

We can use the  Pythagorean theorem

a^2+b^2 = c^2

where a and b are the legs and c is the hypotenuse  to find the  diagonal

2^2 + (sqrt(20))^2 = c^2

4+20 = c^2

24 = c^2

Taking the square root of each side

sqrt(24) = c

4.898979486=c

Rounding to the nearest tenth

4.9 =c

The correct statement for a monopolistic competitor in long-run equilibrium is: p = ATC = MC = MR. The correct answer is B.

In long-run equilibrium, a monopolistic competitor maximizes its profit by setting its marginal cost (MC) equal to its marginal revenue (MR) and producing the quantity where MC = MR. At this quantity, the firm charges a price (p) equal to the average total cost (ATC) to cover all its costs.

By setting the price equal to the average total cost and producing where marginal cost equals marginal revenue, the monopolistic competitor achieves a balance between maximizing profits and covering costs. This equilibrium condition ensures that the firm does not have the incentive to enter or exit the market in the long run, as it is earning normal profits.

Therefore, The correct answer is B. p = ATC = MC = MR.

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The linearly independent solution of the non-homogeneous equation is y = y-c + y-p, y = c1×(x²(-1/2)cos(x)) + c2×(x²(-1/2)sin(x)) + (8/35)×x²(3/2) + (2/35)×x²(-1/2) where c1 and c2 are arbitrary constants.

The associated homogeneous equation is: x²2y'' + xy' + (x²2 - 1/4)y = 0

The complementary solution can be found by assuming y has the form y-c = c1y1 + c2y2, where c1 and c2 are constants, and y1 and y2 are the given linearly independent solutions.

y-c = c1×(x²(-1/2)cos(x)) + c2×(x²(-1/2)sin(x))

Now, the particular solution, denoted as y-p, of the non-homogeneous equation.

y-p has the form:

y-p = Ax²(3/2) + Bx²(-1/2)

where A and B are constants to be determined.

The first and second derivatives of y-p:

y-p' = A×(3/2)x²(1/2) - (1/2)Bx²(-3/2)

y-p'' = A(3/4)×x²(-1/2) + (3/4)Bx²(-5/2)

Substituting these into the non-homogeneous equation:

x²2y_-p'' + xy-p' + (x²2 - 1/4)×y-p = x²(3/2)

x²2×(A×(3/4)x²(-1/2) + (3/4)Bx²(-5/2)) + x(A×(3/2)x²(1/2) - (1/2)Bx²(-3/2)) + (x^2 - 1/4)(Ax²(3/2) + Bx²(-1/2)) = x²(3/2)

Simplifying and collecting like terms:

(3A/4)x²(3/2) + (3B/4)x²-1/2) + (3A/2)x²(3/2) - (1/2)Bx²(3/2) + (A - (1/4))x²(5/2) + (B/4)x²(1/2) - (A/4)x²(-1/2) + Bx²(-3/2) = x²(3/2)

Matching the coefficients of like powers of x:

[(3A/4) + (3A/2) - (1/2)B]x²(3/2) + [(3B/4) + (B/4)]x²(-1/2) + [(A - (1/4))]x²(5/2) + [(-A/4) + B]x²(-1/2) + [B/4]x²(-3/2) = x²(3/2)

Equating the coefficients of x²(3/2) on both sides:

(3A/4) + (3A/2) - (1/2)B = 1

(9A/4) - (1/2)B = 1

Equating the coefficients of x²(-1/2) on both sides:

[(3B/4) + (B/4)] - (A/4) = 0

(4B/4) - (A/4) = 0

Simplifying the equations:

(9A - 2B) = 4

4B - A = 0

Solving these equations simultaneously ,A = 8/35 and B = 2/35.

Therefore, the particular solution is: y-p = (8/35)×x²(3/2) + (2/35)×x²(-1/2)

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