a normal population has a mean of 59.8 and a standard deviation of 18.0. a sample of 10 will be taken. find the probability that the sample mean will be greater than 59.8. a) calculate the z score. (round your answer to 2 decimals.) b) find the probability that the sample mean will be greater than 59.8. (round your answer to 4 decimals.)

Answer:

B

Step-by-step explanation:

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Hello!

b = 3 - 2a

b = 3 - 2*4

b = 3 - 8

b = -5

It should be noted that the volume of the pyramid will be 14.8 unit³.

From the information given, the solid right pyramid has a regular hexagonal base with an area of 7.4 units².

The height of the pyramid is also 6 units.

Therefore, the volume of the pyramid will be

= 1/3 × Area of the base × height

= 1/3 × 7.4 × 6

= 14.8 units³

In conclusion, the volume of the pyramid is 14.8 unit³.

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Answer:600

Step-by-step explanation:

Answer:

20

___ x X = 120

100

x100       x 100

20x = 120

divide by 20 on both sides.

x = 6

The critical t-value is approximately 1.753.

To find the critical value for a 96% confidence interval with a sample size of 15, we need to determine the t-value from the t-distribution table. The t-distribution table is a statistical tool used to determine the probability of a t-value given the degrees of freedom (df) and the desired level of significance (α).

In this case, we have a sample size of 15, which means our degrees of freedom are 14 (n - 1). Looking at a t-distribution table for 14 degrees of freedom and a 96% confidence interval.

This means that if we were to construct a confidence interval from a sample size of 15, the margin of error would be calculated by multiplying the critical t-value of 1.753 by the standard deviation of the sample and dividing by the square root of the sample size. The resulting interval would contain the population mean with 96% confidence.

It's essential to note that the critical value will change as the sample size and confidence level change. Therefore, it's crucial to use the correct table to find the corresponding critical values for a given dataset's sample size and confidence level.

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The conditional probability values are 0.57 and 0.43

               Has Eaten before   Have not           Total

Snack A     144                               108                252

Snack B      92                               228                320

Total          236                              336                572

Using the data in a table, the company that makes snack A calculates probabilities related to a random selected person.

The required probabilities are conditional probabilities, and they are calculated using:

P(A | B) = P(A and B)/P(B)

Using the above formula, we have:

The probability that a customer eats snack A given that the customer has eaten snack A before, to be:

P = n(Have eaten snack A)/n(Snack A)

This gives

P = 144/252

Evaluate

P = 0.57

Also, we have:

The probability that a customer eats snack A given that the customer has not eaten snack A before, to be:

P = n(Have not eaten snack A)/n(Snack A)

This gives

P = 108/252

Evaluate

P = 0.43

Hence, the probabilities are 0.57 and 0.43

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The formula for the distributive property is: a(b+c) = ab + ac.

When performing arithmetic operations, the numbers in mathematics should adhere to the characteristic quality. The many qualities include those that are associative, commutative, distributive, inverse, identity, and so on. The ability to multiply a number by a set of numbers that are added together is known as the distributive property.

According to this property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.

Thus, The formula for the distributive property is: a(b+c) = ab + ac.

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Answer:

49.5

Step-by-step explanation:

11 times 3 is 33 so if you take 33 times 1.5 it is 49.5

Answer:

????????????????????

Step-by-step explanation:

Ummmm????????????????

Answer:

cos a = \(\frac{7}{25}\)

Step-by-step explanation:

Given

sin a = \(\frac{24}{25}\) = \(\frac{opposite}{hypotenuse}\)

tan a = \(\frac{24}{7}\) = \(\frac{opposite}{adjacent}\)

Then this is a right triangle with opposite = 24, adjacent = 7 and hypotenuse = 25 , then

cos a = \(\frac{adjacent}{hypotenuse}\) = \(\frac{7}{25}\)

The percent decrease in price for booking early for a spring break vacation package is 16.5%.

This was calculated by taking the amount of money saved ($35) and dividing it by the original price of the package ($209.99). Then, the resulting decimal was multiplied by 100 to convert it into a percentage.

Mathematically, the calculation looks like this:

(35/209.99) ×100 = 16.5%.

The 16.5% decrease in price is a substantial savings and could be used to purchase additional items or activities during the vacation. Booking early is often a great way to save money on vacation packages, since travel agents and companies often lower the prices to incentivize travelers to book in advance.

It is important to remember, however, that the savings may not always be 16.5%. Depending on the travel agent or company, the percentage of savings may vary. Additionally, some packages may not offer any savings at all. Therefore, it is important to do research and compare different packages before booking.

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Answer:

Hugo salió con Susan, Coco salió con Pamela y Manuel salió con Nancy.

Step-by-step explanation:

Dado que a una reunión asistieron tres amigos: Manuel, Hugo y Coco; y tres damas: Pamela, Nancy y Susan, y terminada la actividad, cada uno de los muchachos salió acompañado por una dama, y Hugo salió con la amiga de Nancy, mientras que Pamela, que no simpatiza con Nancy, salió antes que Manuel, para determinar con quién salió cada persona debemos realizar el siguiente razonamiento lógico:

Hugo = Amiga de Nancy (no es Pamela) = Susan

Pamela = Sale antes que Manuel (no sale con Hugo) = Coco

Nancy = Manuel

Por lo tanto, Hugo salió con Susan, Coco salió con Pamela y Manuel salió con Nancy.

Answer:

1, volume=23×9×5

=1035

2, volume=(1/2×5×4)×20

... =200

3.

1) Use the formula of rectangular prism: width x height x length

2) Use the formula of triangular prism: (Base x height x length) ÷ 2

3) Use the formula of cylinder: π x \(radius^{2}\) x height

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

1)

width x height x length

= 5 x 9 x 23

= 1035

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

2)

(Base x height x length) ÷ 2

= (5 x 4 x 20) ÷ 2

= 400 ÷ 2

= 200

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

3)

π x \(radius^{2}\) x height

= π x \(2.5^{2}\) x 12

= π x 6.25 x 12

= 75π

= 236 (rounded to neareast whole number)

Answer:

A) x=2

Step-by-step explanation:

Answer:

it is simply 4 weeks

Step-by-step explanation: 7 x 4 = 28 so 28 divided by 7 = 4 so your answer is 4 whole weeks.

Answer:

4 weeks

Step-by-step explanation:

28= days

Q.How many weeks?

P.S : 7= no.of days in a week

= 28/7 weeks

=4 weeks

Answer:

Step-by-step explanation:

The question doesn't seem complete, but the question is likely to ask for 2 things: the equation of the ellipse and it's foci. So I'll respond to that. Also, the ellipse will be at the center since the artist wants the largest.

Firstly, the equation of an ellipse at the center is given by:

(x²/a²) + (y²/b²) = 1 where a > b.

Since the artist wants to make the largest ellipse, then the length of the rectangle will be the length of the ellipse, same applies to the width.

Since the length is 60, then a = 60/2 = 30

Since the width is 40, then b = 40/2 = 20

Therefore, the equation of the ellipse is:

(x²/30²) + (y²/20²) = 1

To find the foci we need to know the center and this can be gotten by

c² = a² – b²

c² = 30² – 20² = (30 + 20)(30 – 20) = (50)(10) = 500

c = √(500) = 10√(5).

The foci, since it's at th center would be:

(–10√(5), 0) and (+10√(5), 0)

The largest ellipse that the artist can make on the considered rectangular wooden piece will have area as: \(\dfrac{x^2}{900} + \dfrac{y^2}{400} = 1\\\)(assuming its major and minor axes lie on x and y axis respectively)

Suppose that the major axis is of the length 2a units, and that minor axis is of 2b units, then if major axis is on x-axis and minor axis is on y-axis, then the equation of that ellipse would be:
\(\dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} =1\)

For this case, as we have rectangular piece of board the maximum ellipse will have it's major axis of length 60 inches, and of minor axis as 40 inches.

Thus, we have:

\(a = 60/2 = 30\: \rm inches\\b = 40/2 = 20 \: inches\)

Thus, if the rectangle is placed such that the major axis is on x-axis, and minor axis is on y-axis, then the equation of that ellipse would be:

\(\dfrac{x^2}{30^2} + \dfrac{y^2}{20^2} = 1\\\\\dfrac{x^2}{900} + \dfrac{y^2}{400} = 1\\\)

Thus, the largest ellipse that the artist can make on the considered rectangular wooden piece will have area as: \(\dfrac{x^2}{900} + \dfrac{y^2}{400} = 1\\\)(assuming its major and minor axes lie on x and y axis respectively)

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Answer

Quadrant I

Step-by-step explanation

Hence, point A is located on the Quadrant I

We would have 95 observations available for estimation, assuming that we use all available past data.

Assuming that the time series data set has observations at a fixed time interval (e.g., yearly data), and the distributed lag model of order 5 is estimated using only past observations (not future ones), the number of observations available for estimation will depend on the lag length.

Here we have to use regression with time. For a distributed lag model of order 5, we need to use the past 5 observations of the dependent variable as predictors in addition to any other explanatory variables included in the model.

If we use all available past observations (up to 100 years), then we can estimate the model for up to 95 years of data. This is because we need at least 5 observations to estimate a distributed lag model of order 5.

Therefore, there will be 95 observations available for estimation

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Answer:

1.3 cups

Step-by-step explanation:

Answer:

91.7 inches to 1 decimal place

Step-by-step explanation:

We will use Pythagoras's theorem to find the height of the pyramid.

The height of the Pyramid forms a right-angled triangle with half of the base and the slant height.

We can get half the length of the base by dividing the length of one side of the base = 20.4 by 2 = 10.2in

slant height = 92.3in

Therefore height = \(\sqrt{92.3^{2} -10.2^2} =91.73in\)

The height of the pyramid is 91.73inches to 1 decimal place

Answer:

1.6

So one whole orange and a sixth of another orange

Step-by-step explanation:

The equation of the hyperbola on which the ship is positioned is x²/2025-y²/4375=1

Given that radio stations, A and B are 160 kilometers apart and the signal from B arrives 0.0003 seconds before the signal from A and the signal travels 300,000 kilometers per second.

The distance between radio station A and B are d=160 km.

The time is t=0.0003s.

The speed of the signal travel is v=300000 km/s.

Consider both radio stations A and B lie at foci on the x-axis.

The origin lies at the midpoint between the stations.

The distance of one of the stations from the origin is,

c=d/2

c=160km/2

c=80km

The centre of the hyperbola lies at (0,0), so both stations lie at coordinates points of (-80,0) and (80,0).

The expression for the difference in distance is,

I=vt

I=300000×0.0003

I=90km

The semi-major axis of the hyperbola is,

a=I/2

a=90km/2

a=45km

The expression for the semi-minor axis of the hyperbola is,

b²=c²-a²

b²=(80)²-(45)²

b²=6400-2025

b²=4375

The expression for the hyperbola on which the ship is positioned,

x²/a²-y²/b²=1

x²/(45)²-y²/4375=1

x²/2025-y²/4375=1

Hence, the equation of hyperbola on which the ship is positioned for radio stations, A and B are 160 kilometers apart and signal from B arrives 0.0003 seconds before the signal from A is x²/2025-y²/4375=1.

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Using proportional relationships, we can say that They will walk 12 laps and run 20 laps for a total of 32 miles.

In a direct proportional relationship, the output variable is found by the multiplication of the input variable and the constant of proportionality k, as follows:

y = kx.

Given that we know this, they walk 3/8 of the 8 miles that make up the complete distance. Run 5/8 of the route.

The following are the proportional relationships for the distances:

For a total distance of 32 miles, the distances walked and run are given:

therefore, They will walk 12 laps and run 20 laps for a total of 32 miles as per the proportional relation.

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The number of cases per batch that should be produced to minimize cost is: 300 units

The number of cases per batch that should be produced to minimize cost can be found by using the Economic Order Quantity.

The Economic Order Quantity (EOQ) is a calculation performed by a business that represents the ideal order size that allows the business to meet demand without overspending. The inventory manager calculates her EOQ to minimize storage costs and excess inventory.  

Thus:

Number of cases per batch = √((2 * Setup costs * annual demand)/ holding costs for the year)

Solving gives:

√((2 * 30 * 15000)/10)

= √90000

= 300 units

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Answer:

f(t) = -16t^2 + 180

f(0) = 180, f(1) = 164 = 180 - 16,

f(2) = 116 = 180 - 64, f(3) = 36 = 180 - 144

Table B is the correct table.

Answer:

The correct choice is D.

Answer:

i may be wroung but it should be 90

Step-by-step explanation:

Answer:

x=35

Step-by-step explanation:

The sum of angles in a triangle is equal to 180. In the triangle given, we have to add all the angles to find x.

So,

\(3x+x+40=180\)

to find x, we must isolate it:

combine common terms:

\(4x+40=180\)

subtract the 40 to both sides:

\(4x+40-40=180-40\)

divide by three to isolate the variable:

\(4x/4=140/4\)

and the resulting would be our x:

\(x=35\)

to check if our answers make sense, substitute.

\(3(35)+35+40=180\)

solve:

\(180=180\)

that's it! hope it helps :)

• Let's call A the event of a bow tie designed with swirls (P(A)=0.3).

• Let's call B the event of a bow made of velvet (P(B)=0.1).

It is important to know that the events are mutually exclusive because bows can be made of two different materials at the same time. which means there's no intersection between A and B. So, the probability is

Answer:

14

Explanation:

To evaluate the expression, we need to replace x by 4. So, the expression is equal to:

3x + 2

3(4) + 2

12 + 2

14

Therefore, the value of the expression is 14

a) distance

b) displacement

c) scalar

d) vector