7. Notice the right triangle inside the pyramid. Given a hypotenuse of 10 in and leg of 8
in, use the Pythagorean Theorem to find the true height (H) of the pyramid. What is
the volume of the pyramid?

The function g(x) is a quadratic function in vertex form. Its vertex is at (3, 9), and it opens upwards because the coefficient of the squared term is positive.

The function f(x) is also a quadratic function, but in standard form. It opens upwards because the coefficient of the squared term is positive.

Since both functions have a minimum value at the vertex, the graphs of g(x) and f(x) will be similar in shape. However, the vertex of f(x) is at (0,0), so it is shifted to the left of g(x). Also, the y-intercept of f(x) is (0,0), while the y-intercept of g(x) is (0,18).

In summary, the graph of g(x) is the graph of f(x) shifted 3 units to the right and 9 units up.

The plan which generate the most interest after three years is 5.0% compounded semi-annually, the correct option is A

If the initial amount (also called as principal amount) is P, and the interest rate is R% per unit time, and it is left for T unit of time for that compound interest, then the interest amount earned is given by:

[tex]CI = P\left(1 +\dfrac{R}{100}\right)^T - P[/tex]

The final amount becomes:

[tex]A = CI + P\\A = P\left(1 +\dfrac{R}{100}\right)^T[/tex]

Given that;

The amount of investment= $4,500

Now,

The amount with rate of 5.0% compounded semi-annually;

The final balance is ₹5,218.62.

The total compound interest is ₹718.62.

The amount with rate of 4.9% compounded quarterly;

The final balance is ₹5,207.94.

The total compound interest is ₹707.94.

The amount with rate of 4.8% compounded monthly;

The final balance is ₹5,195.49.

The total compound interest is ₹695.49.

The amount with rate of 5.1% compounded yearly;

The final balance is ₹5,209.31.

The total compound interest is ₹709.31.

Therefore, maximum compound interest will be of 5% semi annually.

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The company's profit in 2017, modeled by the given function, was $193651949.5

The equation of the function is given as

P(t) = 0.5t^6 − 3t³ +t² +25

First, we calculate the value of t in 2017

t = 2017 - 1990

t = 27

Using the Remainder theorem

To find the company's profit in 2017, we need to substitute t = 27 in the given function P(t):

P(27) = 0.5(27)^6 - 3(27)^3 + (27)^2 + 25

Evaluate

P(27) = 193651949.5

Therefore, the company's profit is $193651949.5

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The probability of getting more than 5 questions right in the quiz is

0.00011445.

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are.

the probability of guessing right on a 4-option multiple choice item is= 1/4

= 0.25

A quiz contains 10 questions.

now, the probability of getting 5 right answers as below,

Required Probability = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)

so, this is the probability to come right answers,

Required Probability  = (1/4)^6 (3/4)^4 + (1/4)^7 (3/4)^3 + (1/4)^8 (3/4)^2 + (1/4)^9 (3/4)^1 + (1/4)^10

Required Probability = 0.000077 + 0.000025 + 0.0000086 + 0.0000029 + 0.00000095

after adding all values we get the required probability,

Required Probability = 0.00011445.

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the complete and correct question is ,

the probability of guessing right on a 4-option multiple choice item is 1/4 or 0.25. a quiz contains 10 questions. find the probability of getting more than 5 right.

The weighted average is 86. To calculate the weighted average, we first need to find the contribution of each score to the total grade based on their weightage.

Lab score contribution = 0.17 x 95 = 16.15

First major test contribution = 0.25 x 68 = 17

Second major test contribution = 0.25 x 95 = 23.75

Final exam contribution = 0.33 x 81 = 26.73

Total contribution = 16.15 + 17 + 23.75 + 26.73 = 83.63

Therefore, the weighted average is 83.63/0.8 = 86.

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Answer:

Outliers are points that are on the very edge of a scatter plot, separated from the other points.

Step-by-step explanation:

The probability of picking one ball of each color is 10/19. The probability of picking a red ball with a number one less than the number on the black ball is 9/190.

(I) To figure the probability of picking one repudiate and one red ball, we can separate it into two cases: first, picking a debase and afterward a red ball, and second, picking a red ball and afterward a renounce.

The probability of picking a torpedo on the principal draw is 10/20 (since there are 10 renounces and 20 all out balls), and the probability of then picking a red ball on the subsequent draw is 10/19 (since there are currently 9 red balls avoided with regards to a sum of 19 balls). So the probability of picking a repudiate first and afterward a red ball is (10/20) * (10/19) = 1/19.

Essentially, the probability of picking a red ball first and afterward a torpedo is (10/20) * (10/19) = 1/19.

Hence, the probability of picking one chunk of each tone is the amount of these two probabilities: 1/19 + 1/19 = 2/19.

Notwithstanding, we want to isolate by 2 to represent the way that we might have picked the balls in the contrary request nevertheless have one chunk of each tone. So the last probability is (2/19)/2 = 10/19.

Consequently, the probability of picking one wad of each tone is 10/19.

(ii) To figure the probability of picking a red ball with a main not exactly the number on the debase, we can initially fix the renounce that we pick. There are 10 decisions for the renounce. The main red ball with a main not exactly the torpedo is the red ball with the following most minimal number, so there is just a single decision for the red ball.

In this manner, the probability of picking a debase and afterward a red ball with the number on the red ball one not exactly the number on the repudiate is (10/20) * (1/19) = 1/190.

We really want to duplicate this by 9, since there are 9 sets of contiguous numbers (1 and 2, 2 and 3, ..., 9 and 10) for which the condition is fulfilled. So the last likelihood is 9/190.

Thusly, the probability of picking one chunk of each tone, with the number on the red ball being one not exactly the number on the debase, is 9/190.

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The distribution used to obtain the critical value in this situation is the Student's t-distribution.

Critical value is a statistical value used to determine whether a hypothesis test result is statistically significant or not. It is the value that is compared to the test statistic to determine whether the null hypothesis should be rejected or not. The critical value is determined by the level of significance chosen for the study, the sampling distribution of the test statistic, and the degrees of freedom.

The Student's t-distribution is a symmetric probability distribution that is used when the population standard deviation is unknown. It is used in situations where there is a small sample size (less than 30) and the sample is drawn from a normally distributed population. In this case, the owner is interested in developing a 90% confidence interval estimate, so the critical value will be obtained from the Student's t-distribution.

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The value of f( -10 ) in the piecewise function is 150.

A piecewise function is simply a function which has different definitions of values for different intervals.

Given the piecewise function;

         t² - 5t; t ≤ -10

f(t) = { t + 19; -10 < t < -2

         t³/( t + 9 ); t ≥ -2

To solve for f( -10 ), we check the interval where -10 falls into.

Since -10 is less than or equal to -10, it falls in the interval of t ≤ -10.

Hence;

f(t) =  t² - 5t

Replace t with -10 and simplify.

f( -10 ) =  ( -10 )² - 5( -10 )

f( -10 ) =  100 + 50

f( -10 ) =  150

Therefore, the value of f( -10 ) is 150.

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To prove by contrapositive, we need to show that if n is odd, then n^3+5 is even.

The contrapositive of the original statement is logically equivalent to the original statement.  if we can prove the contrapositive, then we have also proven the original statement.

Proof by contrapositive:

Assume that n is an odd integer, which means that n can be written in the form n = 2k + 1, where k is an integer.

Then, n^3+5 = (2k+1)^3 + 5

= 8k^3 + 12k^2 + 6k + 1 + 5

= 8k^3 + 12k^2 + 6k + 6

We can factor out a 2 from the last two terms of this expression:

n³ + 5 = 2(4k³ + 6k²)

Since 4k³ + 6k² + 3k + 3 is an integer, we can see that n³ + 5 is an even integer, which means that n is even by definition.

we have proven that if n is an integer and n³ + 5 is odd, then n is even by contrapositive.

n^3+5 = 2(4k^3 + 6k^2 + 3k + 3)

Since 4k^3 + 6k^2 + 3k + 3 is an integer, n^3+5 is even.

we have shown that if n is odd, then n^3+5 is even, which is the contrapositive of the statement we were asked to prove.

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The length of the incline plane is equivalent to 13.9ft

Application of Pythagoras theorem

According to the theorem, the square of the hypotenuse is equal to the sum of the square of the adjacent and opposite

c^2 = a^2 + b^2

From the given question, the length of the incline is the hypotenuse 'c' where:

a = 7ft

b = 12ft

Substitute

c^2 = 7^2 + 12^2

c^2 = 49 + 144

c^2 = 193

x = 13.9ft

Therefore the length of the inclined plane is 13.9ft

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Answer: volume would be 56

Step-by-step explanation:

Volume = length X width X height

The second sock picked is dependent on the first. The probability of picking a white sock for the left foot and a brown sock for the right foot without replacing the first sock is 1/12.

To calculate the probability of picking a white sock for the left foot and a brown sock for the right foot without replacing the first sock, we first need to count the total number of possible outcomes. There are 8 socks in the drawer: 2 white, 6 brown, and 4 black. Since we are picking two socks without replacing the first, the total number of possible outcomes is 8C2 = 28.

Next, we need to count the number of favourable outcomes. In this case, there is only one favourable outcome: picking a white sock for the left foot and a brown sock for the right foot.

Therefore, the probability of picking a white sock for the left foot and a brown sock for the right foot without replacing the first sock is 1/28.

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The median for the distribution table is falls within the range of 60-70 points.

Understanding the concept of median is crucial in analyzing data and making statistical inferences.

From the given distribution table, we can see that the percentage of students scoring between 0-60 points is 15%, between 60-70 points is 10%, between 70-80 points is 25%, between 80-90 points is 30%, and between 90-100 points is 20%. To calculate the cumulative percentage, we can add up the percentages from left to right.

For instance, the cumulative percentage of students scoring between 0-70 points is

=> 15% + 10% = 25%.

Similarly, the cumulative percentage of students scoring between 0-80 points is

=> 15% + 10% + 25% = 50%.

We can repeat this process to find the cumulative percentage for each score range.

Once we have the cumulative percentages, we can find the median score. In this case, since the total percentage is 100%, the median score would be the point at which the cumulative percentage reaches 50%. We can use the height column to calculate this value.

Starting from the lowest score range, we can add the heights until the cumulative percentage exceeds 50%. The point where this happens is the median score.

Moving on to the next score range, the cumulative percentage for scores between 0-70 points is 25%, which is greater than 50%. Therefore, the median score falls within the range of 60-70 points.

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Complete Question:

A distribution table for the scores on an exam is shown below. The second row says that 10% of the students scored between 60 and 70. Fill in the blanks in the height column. Do not include units.

Points (Width) % 0-60  60-70 70-80 80-90 90-100

(Area) Height=Area/Width (% per point)  15  10  25 30  20

What is the median score?

What is the slope of the budget line if the slope of the budget line equals the slope of the indifference curve when consumer equilibrium is taken into account on an indifference curve/budget line diagram

A client selects a group of items where an indifference curve is perpendicular to the price range line in order to optimize utility. The fee ratio of the two things is the same as the client's marginal charge of substitution (absolutely the cost of the slope of the indifference curve) at the utility-maximizing solution. The marginal charge of substitution is the indifference curve's slope (MRS). The MRS is the price at which a client will often trade one fact for another.

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A, B, and C's interest rates are 49.96, 296.32 and 102.96, respectively. Since the total interest is $449.24.

The annual percentage rate (APR) on a credit card indicates that the interest you pay over a year is generally equivalent to your balance.

The balances and annual percentage rates for Jimmy's credit cards are shown below.

If Jimmy pays the same amount each month, he will be free of his credit card debt in a year.

We know that the formula

[tex]$P V=\frac{P M T\left[1-\left(1+\frac{r}{12}\right)^{12 n}\right]}{\frac{r}{12}}$[/tex]

Where, PV be present value

PMT be monthly payment

r be interest rate

n be time

For credit card A, we have

[tex]$\begin{aligned} 563 & =\frac{{PMT}\left[1-\left(1+\frac{0.16}{12}\right)^{12}\right]}{\frac{0.16}{12}} \\ \text { PMT } & =51.08\end{aligned}$[/tex]

Total payment will be, 51.08 × 12 = 612.96

The interest charge will be, 612.96 − 563 = 49.96

For credit card B, we have

[tex]$\begin{aligned} & 2525=\frac{{PMT}\left[1-\left(1+\frac{0.21}{12}\right)^{12}\right]}{\frac{0.21}{12}} \\ & \mathrm{PMT}=235.11\end{aligned}$[/tex]

Total payment will be, 235.11 × 12 = 2821.32

The interest charge will be, 2821.32 − 2525 = 296.32

For credit card C, we have

[tex]$\begin{aligned} 972 & =\frac{\text { PMT }\left[1-\left(1+\frac{0.19}{12}\right)^{12}\right]}{\frac{0.19}{12}} \\ \text { PMT } & =89.58\end{aligned}$[/tex]

Total payment will be, 89.58 × 12 = 1074.96

The interest charge will be, 1075.96 − 972 = 102.96

Total interest = 102.96 + 296.32 + 49.96

Total interest = 449.24

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Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

By adding together the specific amounts the chef used in each recipe, one can determine the total number of cups of milk she consumed. In order to achieve this, we can condense the phrase:

1/4 + (2 x 5) = 1/4 + 10

The two amounts on the right side of the equation can then be added:

1/4 + 10 = 10.25

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Answer:

I will tell you the answer

Step-by-step explanation:

Answer:

the median is 11 questions.

Step-by-step explanation:

khan academy :)

Answer:

Step-by-step explanation:

[tex]\sqrt{6} * \sqrt{3}\\ \sqrt{18}, 18=9*2, \\ \sqrt{9*2}, \\ \sqrt{9*2} = \sqrt{9} * \sqrt{2}, \sqrt{9}=3\\ 3 \sqrt{2}[/tex]

B.

The conditional expectation of αX given Y=y is (αλy / β + αλ)^α * e^(-(β+αλ)/βy) and the Law of Iterated Expectation gives E[αX] = (αλ / β + αλ)^α * (β / (β+αλ))^α * (Γ(α) / β).

Let X be a Poisson random variable with parameter λ and Y be a Gamma random variable with parameters α and β. We want to find the conditional expectation of αX given Y=y and then apply the Law of Iterated Expectation to find E[αX].

The conditional probability density function of αX given Y=y is:

fX|Y(x|y) = P(X=x|Y=y) = P(X=x,Y=y) / P(Y=y)

Since X and Y are independent, we have:

P(X=x,Y=y) = P(X=x)P(Y=y)

Therefore, the conditional probability density function of αX given Y=y is:

fX|Y(x|y) = (λ^x/x!) * (β^α / Γ(α)) * y^(α-1) * e^(-βy) / (λ^y * e^(-λ) * β^α / Γ(α))

fX|Y(x|y) = (λ^x / x!) * (y^α * e^(-βy)) / (Γ(α) * λ^y * β^α)

Now we can calculate the conditional expectation of αX given Y=y:

E[αX|Y=y] = ∑ x=0^∞ αx * fX|Y(x|y)

E[αX|Y=y] = ∑ x=0^∞ αx * (λ^x / x!) * (y^α * e^(-βy)) / (Γ(α) * λ^y * β^α)

E[αX|Y=y] = (αλy / β + αλ)^α * e^(-(β+αλ)/βy)

Now we can apply the Law of Iterated Expectation to find E[αX]:

E[αX] = E[E[αX|Y]]

E[αX] = E[(αλY / β + αλ)^α * e^(-(β+αλ)/βY)]

Since Y is a continuous random variable, we need to integrate over all possible values of Y:

E[αX] = ∫ 0^∞ (αλy / β + αλ)^α * e^(-(β+αλ)/βy) * (β^α / Γ(α)) * y^(α-1) * e^(-βy) dy

E[αX] = (αλ / β + αλ)^α * (β / (β+αλ))^α * (Γ(α) / β)

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Pixel size for fast spin echo is 0.94mm x 0.94mm. FOV 30cm, TR 600, TE 10, 320x320 matrix, 4NEX, 3mm slice thickness, 3ETL.

To calculate the pixel size, we first need to convert the FOV from 30cm to 300mm. We can then divide the FOV by the matrix size (320 x 320) to get the pixel size. This will give the same value for both the phase dimension and frequency dimension pixels. So the pixel size for the fast spin echo sequence is 0.94mm x 0.94mm.

The other parameters for the sequence are TR 600, TE 10, 4NEX, 3mm slice thickness and 3ETL. These parameters will determine the type of sequence and the overall image quality. With these parameters, the fast spin echo sequence should produce a high quality image with good resolution.

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Now we can find the area:

Area = length x width

Area = (19/4) x 6

Area = 114/4

Area = 28.5

Therefore, the area of the picture is 28.5 square inches.

The area of a planar figure is the region that its perimeter includes. The quantity of unit squares that completely encircle the surface of a closed figure is its area. Square units like cm2 and m2 are used to measure area.

The area of a rectangle is found by multiplying its length by its width. In this case, the width is 6 inches and the length is 4 3/4 inches. We can convert the length to an improper fraction to make it easier to multiply:

4 3/4 = 19/4

Now we can find the area:

Area = length x width

Area = (19/4) x 6

Area = 114/4

Area = 28.5

Therefore, the area of the picture is 28.5 square inches.

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The area of the rectangular picture painted by Tamara is 28.5 in.²

What is a rectangle?

The internal angles of a rectangle, which has four sides, are all precisely 90 degrees. The two sides come together at a straight angle at each corner or vertex. The rectangle differs from a square because its two opposite sides are of equal length. Rectangles are flat, two-dimensional shapes. The diagonals of the rectangle's symmetrical shape are of equal length. The rectangle will be split into two right-angle triangles by a diagonal.

The region covered by a two-dimensional plane is known as its area. It has a square unit of measurement. As a result, the rectangle's area is the space enclosed by its exterior lines. It is the same as the length times the width calculation.

Given,

  The width of the rectangular picture = 6 inches

The length of the rectangular picture = 4 3/4 inches = 19/4 inches

The area of the picture = Area of the rectangle = Length * breadth

                                                                      = 19/4 * 6 = 57/2 = 28.5 in.²

Therefore the area of the rectangular picture painted by Tamara is

28.5 in.²

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Answer:

False

Step-by-step explanation:

This statement is false.

The set of whole numbers include the set of Natural numbers "N" = {1, 2, 3, 4, 5, 6, ...}, the set of the negatives of the natural numbers: {-1, -2, -3, -4,...}, and the zero: {0}

We see then that the set of Natural numbers is a subset of the set of whole numbers Z = {... -4,-3,-2,-1, 0,1, 2, 3, 4, 5, ...}

Answer: i think False

Step-by-step explanation: why not pick false…..

Hope this helps^^

The difference in the production levels will be 3x + 8.

The amount that Jackson spent more will be 5.20 - p.

An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.

Based on the information, a company has two manufacturing plants that had levels of 5x + 11 and 2x - 4.

The difference in the production levels will be:

= 5x + 11 - 2x - 3

= 3x + 8

The amount that Jackson spent more will be:

= 7.65 + 5p - 2.45 - 4p

= 5.20 - p.

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Answer:

2 5/8 kg

Step-by-step explanation:

To find the total mass of the 3 parcels, we need to determine the mass of Parcel A and Parcel C.Since Parcel B is the lightest, with a mass of 3/8 kg, and the difference in mass between Parcel A and Parcel C is 1/5 kg, we can say that Parcel A weighs 3/8 + 1/5 = 4/8 = 1/2 kg more than Parcel C.Let's call the mass of Parcel C "x". Then, Parcel A weighs x + 1/2 kg.The total mass of the 3 parcels can be found by adding the masses of all 3 parcels:x + x + 1/2 + 3/8 = 3x + 9/83x = 3 - 9/83x = 27/8 - 9/83x = 18/8x = 6/8 = 3/4 kgSo, the mass of Parcel C is 3/4 kg, the mass of Parcel A is 3/4 + 1/2 = 1 1/4 kg, and the total mass of the 3 parcels is 3/4 + 1 1/4 + 3/8 = 2 5/8 kg.In conclusion, the total mass of the 3 parcels is 2 5/8 kg.

Answer:If A is at point (x,y), then A' would be at point (-x,-y). Same goes for points B and C.

Step-by-step explanation:

The velocity function is written as v(x) = sqrt(x - 3)

The graph is attached

If the velocity of a cruise ship is equal to the square root of the rate of fuel consumption minus 3 units,

Then we can write the velocity function as:

v(x) = sqrt(x - 3),

where

x represents the rate of fuel consumption.

The graph is plotted and attached

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