What is the 14th partial sum of 2,000 − 1,000 + 500 − 250 + ...? Round your answer to the thousandths place.

1,333.252
1,333.333
1,999.878
3,999.756

Answer: 0.2254

Step-by-step explanation:

Let E= Event of getting of female lives in a dorm.

F = Event of getting of female lives in a 'Other'.

From the table , n(E) = 276  and n(F) = 99

and n(E∩F) = 0  [E and F are Mutually exclusive]

Now, n(E∪F)=  n(E) + n(F) - n(E∩F)

= 276+99-0

= 375

also, n(S) =1664       (Sample size)

Required probability : \(P(E\cup F)=\dfrac{n(E\cup F)}{n(S)}\)

\(=\dfrac{375}{1664}\approx0.2254\)

Hence, the  probability that a customer is female and lives in a dorm or is female and lives in 'Other' = 0.2254

9514 1404 393

Answer:

  119

Step-by-step explanation:

Put the given values in the formula for the general term, and do the arithmetic.

  an = a1 +d(n -1) . . . . . first term a1, common difference d

  a14 = 2 +9(14 -1) = 119

The 14th term is 119.

Answer:

The data is:

From the adults in town:

8% have liver problems, of those:

  25% heavy drinkers

  35% social drinkers

  40% non-drinkers.

92% do not have liver problems (100% - 8% = 92%)

   5%  heavy drinkers

   65% social drinkers.

   30% non-drinkers

a) An adult is chosen at random, then:

Has a liver problems

We know that 8% of the adults have liver problems, so the probability is 8%, or 8%/100% = 0.08.

Is a heavy drinker

Out of the 8%, 25% are heavy drinkers, and out of the other 92%, 5% are heavy drinkers, so the total percentage of heavy drinkers is:

(i will use decimal math, because you always should work with decimals instead of percentages)

P = 0.08*0.25 + 0.92*0.05 = 0.066

or 6.6% in percentage form

If a person is found to be a heavy drinker, what is the probability that this person

the proability that some one is a heavy drinker was already found, it is p = 0.066.

Now, of those 0.066 we have:

p1 = 0.08*0.25 = 0.02 have liver problems.

So the probability that, given that some one is a heavy drinker, that her/him also have liver problems is:

P = 0.02/0.066 = 0.3 or 30%.

If a person is found to have liver problems, what is the probability that this person  is a heavy drinker?

]We already know that out of the 8% with liver problems, a 25% are heavy drinkers, so here the answer is 25% or 0.25.

If a person is found to be a non –drinker, what is the probability that this person has  liver problems.

From the 8% with liver problems, we have 40% of non-drinkers,

So the total proportion of non-drinkers with liver problems is:

p1 = 0.8*0.40 = 0.032

From the 92% with no liver problems, we have that 30% of them are non-drinkers, so here we have:

p2 = 0.92*0.30 = 0.276

The total proportion of non drinkers is:

p1 + p2 = 0.032 + 0.276 = 0.308.

Then if we know that some one is non drinker, the proability that the person has liver problems is equal to the quotient between the proportion of non-drinkers with liver problems ( 0.032) and the total proportion of non-drinkers.

p = 0.032/0.308 = 0.104

or 10.4% in percentage form.

When 'x' is 5, the Algebraic  expression 3x - 4 evaluates to 11.

To find the algebraic expression for "4 less than the product of 3 and some number," let's break it down step by step.

First, let's define the unknown number as 'x.' Since the problem states "the product of 3 and some number," we can express this as 3 * x or simply 3x.

Next, we want to subtract 4 from this product. The phrase "4 less than" indicates subtraction, so we subtract 4 from 3x. This can be represented as 3x - 4.

In summary, the algebraic expression for "4 less than the product of 3 and some number" is 3x - 4, where 'x' represents the unknown number.

To calculate the value of this expression for a specific value of 'x,' you substitute that value into the expression and simplify. For example, if 'x' is 5, you would substitute 5 into the expression:

3(5) - 4

This simplifies to:

15 - 4 = 11

So, when 'x' is 5, the expression 3x - 4 evaluates to 11.

In general, the algebraic expression allows us to represent a mathematical relationship between quantities using symbols and operations. By substituting specific values into the expression, we can calculate the corresponding results.

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Note the complete question:

Algebraic expression for 4 less than the product of 3 and some number

What is the algebraic expression for "4 less than the product of 3 and some number?

Please help me understand the meaning of how to calculate.

Answer:

scalene triangle

..... .

Answer:

ypu are going to have to give us a problem to solve or a question.

Step-by-step explanation:

this is a statement

Answer:

19 19/20 in fraction

19.95 as a decimal

Step-by-step explanation:

Answer:

19 and 19/20

Step-by-step explanation:

The bar in a fraction stands for dividing

so you divide 399 by 20 which is 19 and 19 remainder

you turn the remainder into a fraction and the number into a whole number

35 rooms + 3 suites = 38 total rooms.

38 / 4 = 9.5

2 house keepers can clean 9 rooms each and 2 house keepers can clean 10 rooms each

2 Housekeepers need to clean more rooms than the other two.

Hey there! I'm happy to help you!

To solve this, we can set up a proportion below! I will put the data in table, fraction, and ratio form so you can see different ways to visualize it.

                       HEIGHT         LENGTH OF SHADOW

DIXON               ?                              18

ARIADNE           5                              15

                     or

\(\frac{height}{length} =\frac{5}{15} =\frac{h}{18}\)

                     or

5:15= h:18

As we can see, we see that Ariadne's length of shadow is three times as large as her height. Therefore, that means that Dixon's height will be 1/3 of the length of his shadow!

18/3= 6

We can also use the cross multiplying method with our proportion and then solve for h!

h=5*18/15

h=90/15

h=6

Therefore, Dixon is six feet tall.

I hope that this helps! Have a great day!

The last expression finally simplifies to cot β + tan α using quotient identity in trigonometric identities.

We want to verify the trigonometric  identity;

cos (α - β)/(cos α sin β) = cot β + tan α

Now, according to trigonometric identities in mathematics, we know that;

cos (α - β) = (cos α cos β) + (sin α sin β)

Thus, plugging that back into our left hand side of the main question gives;

[(cos α cos β) + (sin α sin β)]/(cos α sin β)

Rewriting this expression by separating the denominator gives;

[(cos α cos β)/(cos α sin β)] + [(sin α sin β)]/(cos α sin β)

Using quotient identities, this can be simplified to;

cot β + tan α

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The domain and the range of the function are given as follows:

The function approaches y = 0 as x approaches positive infinity.

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Answer:

A

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

(x, y)

Left and right affects the x, up and down affects the y.

Since it's a positive 4, it goes up. We can eliminate B and D.

Since it's a positive 8, it goes right. A.

Answer:

X intercept -3, Y intercept, 2

Step-by-step explanation:

The y axis is the vertical line. The x axis is the horizontal line.

Good Luck!

Answer:

It is the first one 1/3(p+45).

Answer:

choice 1) 1/3(p + 45)

Step-by-step explanation:

1/3p + 15 = 1/3(p + 45)

Evaluate the value of expression.

So answer is 782,493,217.8

Answer:

Step-by-step explanation:

In the question we have given volume of Sphere that is 562.5 π in³ and we have asked to find the radius of given sphere. We know that the volume of sphere ,

\( \blue{ \boxed{ \rm{Volume \: of \: Sphere = \frac{4}{3} \pi r {}^{3} }}}\)

So equating it with given volume for finding the radius of sphere :

\( \longmapsto \: \frac{4}{3} \pi r{}^{3} = 562.5\pi\)

Step 1 : Cancelling π as it was present in both side :

\(\longmapsto\:\frac{4}{3} \cancel{\pi }r{}^{3} = 562.5 \cancel{\pi}\)

Step 2 : Transposing 4/3 to right hand side :

\(\longmapsto \: r {}^{3} = 562.5 \times \frac{3}{4} \)

Step 3 : Multiplying 562.5 with 3 :

\(\longmapsto \:r {}^{3} = \frac{1687.5}{4} \)

Step 4 : Dividing 1687.5 by 4 :

\(\longmapsto \:r {}^{3} = 421.875\)

Step 5 : Finding cube root of 421.875

\(\longmapsto \:r = \sqrt[3]{421.875} \)

Step 6 : We get :

\(\longmapsto \: \red{ \boxed{r = 7.5}}\)

Answer:

$365

Step-by-step explanation:

did the math

Answer:

Step-by-step explanation:

x-7

3y+1-7

3y-6

Answer: B

Step-by-step explanation:

'Product' means to multiply, in this case, we are multiplying 50 and n.

Answer:

4x² + 22x - 12

Step-by-step explanation:

A = bh/2

A = (4x - 2)(2x + 12)/2

A = (8x² + 48x - 4x - 24)/2

A = (8x² + 44x - 24)/2

A = 4x² + 22x - 12

The Least common multiple (LCM)  The time at which both bells will ring together is 10:45 am, and the Subsequent times will be 11:30 am, 12:15 pm, 1:00 pm, and so on, with an interval of 45 minutes between each occurrence.

The time at which both bells will ring together, we need to find the least common multiple (LCM) of the intervals at which each bell rings.

The first bell rings every 45 minutes, and the second bell rings every minute. We want to find the point at which both intervals align, meaning they both divide evenly into the same amount of time.

To find the LCM, we can list the multiples of each interval until we find a common multiple.

Multiples of 45 minutes: 45, 90, 135, 180, 225, 270, 315, 360, 405, ...

Multiples of 1 minute: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ...

From the lists above, we can observe that the least common multiple occurs when both intervals coincide at the same time, which is 45 minutes.

Thus, the two bells will ring together every 45 minutes.

If we consider the initial adjustment time of 10:00 am, the first time both bells will ring together is at 10:45 am. After that, they will continue to ring together every 45 minutes throughout the day.

Therefore, the time at which both bells will ring together is 10:45 am, and the subsequent times will be 11:30 am, 12:15 pm, 1:00 pm, and so on, with an interval of 45 minutes between each occurrence.

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Answer: a) To compute the mean of these data, we need to add up all of the ratios and divide by the total number of ratios.

(94+112+78+68+46+111+66+140+428+190+118)/11 = 101.36

The mean is 101.36

b) To compute the median of these data, we need to arrange the data in increasing order and find the middle value.

46, 66, 68, 78, 94, 111, 112, 118, 140, 190, 428

The median is 111

c) The measure that describes the center of this distribution the most accurately is the mean, because it takes into account all of the values in the data set and provides an overall measure of central tendency. The median is also a measure of central tendency but it is affected by the outliers present in the dataset and doesn't provide a good representation of the central value.

Step-by-step explanation:

Answer:

0.00375

Step-by-step explanation:

1.875/500

Answer:

The blue dot is -19

Step-by-step explanation:

Since every 2 ticks are worth 6 (|-10|-|-4|=6), then one tick is worth 3.

We are going backward, so we can count backward.

We have to go down 3 ticks, so -10-3=-13; -13-3=-16; -16-3=-19.

The blue dot is -19

Answer: The blue dot equals to -19.

Step-by-step explanation:

On the number line, there are the numbers -10 & -4.

-7 would fit in the middle of them. That means the number line goes by minus 3.

Count -10 , -13, -16, then you get on the the blue dot which is -19.

Therefore, -19 is the answer.

Answer:

Gradient normal x gradient tangent = -1 is a mathematical expression that relates the normal and tangent vectors of a curve in three-dimensional space. The gradient of a scalar function is a vector that points in the direction of the greatest rate of increase of the function. The normal vector is perpendicular to the surface defined by the function, and the tangent vector is a vector that lies on the surface and points in the direction of the curve.

In mathematics, the cross product of two vectors is a vector that is orthogonal to both vectors, and the magnitude of the cross product is equal to the product of the magnitudes of the two vectors multiplied by the sine of the angle between them. In this case, the normal and tangent vectors of a curve form an orthogonal basis, meaning that they are perpendicular to each other. The expression gradient normal x gradient tangent = -1 says that the magnitude of the cross product of the normal and tangent vectors is equal to -1. This means that the normal and tangent vectors form a right-handed coordinate system, where the cross product is negative because the normal vector points in the opposite direction to the positive z-axis.

Answer:

x = 9

Step-by-step explanation:

6x = 4x + 18

6x - 4x = 18

2x = 18

x = 9

Answer:

-9

Step-by-step explanation:

3x−5x+8x=4x+18

Step 1: Simplify both sides of the equation.

3x−5x+8x=4x+18

3x+−5x+8x=4x+18

(3x+−5x+8x)=4x+18(Combine Like Terms)

6x=4x+18

6x=4x+18

Step 2: Subtract 4x from both sides.

6x−4x=4x+18−4x

2x=18

Step 3: Divide both sides by 2.

2x

2

=

18

2

The coterminal angles for the given angles are:

a. 135 degrees = 495, -225

b. -420 degrees = -60, -780

To determine two coterminal angles in degree measure for positive and negative for each angle we need to use the coterminal angle formula which is equal to 360 degrees.

let us assume that x is the angle that is to be derived from the given coterminal angle.  It is calculated by

coterminal = x ± 360    ............. equation (1)

a. 135 degrees:

substitute x = 135 in the above equation,

coterminal = 135 ± 360

coterminal split = (135 + 360), (135-360)

coterminal split angles = 495, -225

b. -420 degrees:

substitute x = -420  in the above equation,

coterminal = -420  ± 360

coterminal split = (-420 + 360), (-420-360)

coterminal split angles = -60, -780

Therefore we can conclude that coterminal angles for

a. 135 degrees = 495, -225

b. -420 degrees = -60, -780

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