Suppose that an ordinary deck of 52 cards (which contains 4 aces) is randomly divided into 4 hands of 13 cards each. We are interested in determining p, the probability that each hand has an ace. Let
Ei
be the event that the ith hand has exactly one ace. Determine
p=P(E1E2E3E4)
by using the multiplication rule.

This is the formula to solve for the vertex.

Example Question:

Find the vertex of y = -0.5x^2 + 100x

-b/2a = -100/2(-0.5) = -100/-1 = 100

The x coordinate of the vertex is 100.

Best of Luck!

P.S. this is 1000th question i've answered :)

The horizontal distance the plan has covered when it has flown 4,000 feet is 694 feet.

Step-by-step explanation:

Step 1:

For the given triangle, assume the opposite side has a length of x units, the hypotenuse of the triangle measures 4,000 feet. The given angle of the triangle is 10°.  To calculate the opposite side's length of the triangle, we use the sine of the given angle.

[tex]sin A = \frac{oppositeside}{hypotenuse}[/tex]

Step 2:

The length of the opposite side = x feet.

The length of the hypotenuse side = 4,500 feet.

[tex]sin A = \frac{oppositeside}{hypotenuse}, sin 10 = \frac{x}{4000}.[/tex]

[tex]x = sin10 (4000), sin 10 = 0.1736, x = 0.1736(4000) = 694.4 feet[/tex].

So the horizontal distance is 694.4 feet, rounding this off to the nearest foot, we get the horizontal distance as 694 feet.

Explanation:

The sample mean is not always equal to the population mean but if we take more and more number of samples from the population then the mean of the sample would become equal to the population mean.

The Central Limit Theorem states that we can have a normal distribution of sample means even if the original population doesn't follow normal distribution, But we have to take a lot of samples.

Suppose a population doesn't follow normal distribution and is very skewed then we can still have sampling distribution that is completely normal if we take a lot of samples.

Answer: B 8/5 hr

Step-by-step explanation:

One maid can clean the house in 2 hours. This means that the rate at which she cleans the house per hour is 1/2

Another maid can do the job in 8 hours. This means that the rate at which the other maid cleans the house per hour is 1/8

If they work together, they would work simultaneously and their individual rates are additive. This means that their combined working rate would be

1/2 + 1/8 = 5/8

Assuming it takes t hours for both of them to clean the room working together, the working rate per hour would be 1/t. Therefore,

5/8 = 1/t

t = 8/5 hour

Option B is correct. Working together, the two maids can clean the house in 8/5 hours.

Let's assume that the combined rate of both maids working together is x house cleaned per hour. We can set up the equation:

1 maid's rate + another maid's rate = combined rate

1/2 + 1/8 = x

Solving for x:

4/8 + 1/8 = x

5/8 = x

The combined rate of the maids working together is 5/8 house cleaned per hour. To find how long it will take them to clean the house together, we can set up the equation:

(5/8) house per hour = 1 house

Let t be the time it takes them to clean the house together. We can write the equation:

(5/8) * t = 1

Solving for t:

t = 1 / (5/8)

t = 8/5 hours.

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Answer:

[tex]7+6a+5m(4+3a)=0[/tex]

Step-by-step explanation:

We want to simplify the expression

[tex](3 + 3 a ) + (1 + 5 m )(3 + 3 a ) + (1 + 5 m )=0[/tex]

Expanding the expression in the middle

[tex](3 + 3 a ) + 1 (3 + 3 a )+ 5 m (3 + 3 a ) + (1 + 5 m )=0[/tex]

Eliminating all brackets

[tex]3 + 3 a + 3 + 3 a + 15m + 15m a + 1 + 5 m =0[/tex]

Next, we collect our like terms

[tex]3+3+1+3a+3a+15m+5m+15ma=0[/tex]

When you collect like terms, ensure the number of terms are still the same

[tex]7+6a+20m+15ma=0[/tex]

This simplified gives us:

[tex]7+6a+5m(4+3a)=0[/tex]

I caculated it all and it is the same as Newton9022

Hope this helps.

Mrs. Mathewson can serve orange juice to 4 guests. The solution was found by first converting the fractions to the same denominator, then dividing the total orange juice by the amount per guest, and taking into account that you can't serve fractions of a guest.

The problem presented here is a basic division problem that requires you to divide the total amount of orange juice by the amount served to each guest. Mrs. Mathewson has 7/8 quarts of orange juice and she would like to serve each guest 3/16 quarts of orange juice.

Firstly, we'll convert both fractions to the same denominator for simplicity. As 8 is a multiple of 16, we can leave the second fraction as it is (3/16) and change the first fraction to 14/16 (which is the same as 7/8). Now, we divide 14 by 3 which gives us roughly 4.6.

This result means Mrs. Mathewson can serve orange juice to 4 guests with a bit left over. As we can't serve a fraction of a guest, it means she can only serve 4 whole guests.

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Mrs. Mathewson can serve orange juice to 14 guests.

To determine how many guests Mrs. Mathewson can serve orange juice, we need to find the quotient of the total amount of orange juice and the amount per guest. Given that there are 7/8 quarts of orange juice and Mrs. Mathewson wants to serve 3/16 quarts per guest, we divide the total amount by the amount per guest: (7/8) ÷ (3/16) = (7/8) × (16/3) = 14 guests.

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Answer:

Period of 2π

Step-by-step explanation:

The graph of sine starts at zero on the y axis while that of cosine starts at the point 1 as sin 0=0 at t=0 and cos 0=1 at t=0. We say the cosine curve is a sine curve which is shifted to the left by [tex]\frac{\pi}{{2}}\[/tex]

​The basic sine and cosine functions have a period of 2π (in radians). The period is the time it takes to go through one complete cycle. It means that after every complete cycle, the graph repeats itself over and over again..  

Answer:

Check

Step-by-step explanation:

The high and low points repeat in a pattern.

The cycle repeats at equal time intervals.

The swinging motion is smooth, unabrupt.

Answer:

Her hourly rate is $14.

Step-by-step explanation:

Given:

Penelope goes to work after school for 4.5 hours on Mondays, Tuesdays, and Fridays.

She works 8 hours each on Wednesdays or Thursdays.

Now, to find her hourly rate.

So, total hours Penelope work on Mondays, Tuesdays, and Fridays:

[tex]4.5+4.5+4.5=13.5\ hours.[/tex]

And, total hours she work on Wednesdays and Thursdays:

[tex]8+8=16\ hours.[/tex]

Now, the total hours each week she work:

[tex]13.5+16=29.5\ hours.[/tex]

Total money she makes each week = $413.

Now, to get the hourly rate we divide the total hours each week she work by total money she makes each week:

[tex]413\div 29.5[/tex]

[tex]=\$14.[/tex]

Therefore, her hourly rate is $14.

The equation for the resale value of the stereo is V = V0 * e^(-kt), where V0 is the initial value, V is the resale value at time t, and k is the decay constant. Using the given resale value after 4 years, we can solve for k and substitute it back into the equation to find the resale value of the stereo as a function of time.

To find an equation giving the resale value of the stereo as a function of time, we can use the formula for exponential decay: V = V0 * e^(-kt). V0 represents the initial value, V represents the resale value at time t, and k is the decay constant. The given resale value after 4 years is $275, so we can substitute these values into the equation: 275 = 1300 * e^(-4k). To solve for k, divide both sides by 1300 and take the natural logarithm of both sides: ln(275/1300) = -4k. Calculate the logarithm and solve for k to get the decay constant. Finally, substitute the value of k into the equation to get the complete equation for the resale value of the stereo.

Answer:

It depends on what negative number it is. For example -23 is 23 units or whatever to 0.

Step-by-step explanation:

Answer:

p=2

Step-by-step explanation:

Use the slope formula

(p-(-1))/(6-9)=-1

(p+1)/-3=-1

p+1=3

p=2

Answer:

Step-by-step explanation:

Slope, m =change in value of y on the vertical axis / change in value of x on the horizontal axis represent

change in the value of y = y2 - y1

Change in value of x = x2 -x1

y2 = final value of y

y 1 = initial value of y

x2 = final value of x

x1 = initial value of x

The line passes through (9,-1) and (6,p) and the slope is 1

y2 = p

y1 = - 1

x2 = 6

x1 = 9

Therefore,

(p - - 1)/(6 - 9) = - 1

(p + 1)/- 3 = - 1

(p + 1) = - 1 × - 3

p + 1 = 3

p = 3 - 1

p = 2

Answer: its 25 because you're adding the whole line from P to R, so 12.5 + 12.5 is 25

Step-by-step explanation:

P to T is 12.5

T to R is 12.5

Add those together

12.5 + 12.5 gives you 25

Answer:

25 in.

Step-by-step explanation:

In a rectangle the diagonals bisect each other.

Therefore PT = TR = ST = TQ = 12.5 in.

PR = PT + TR = 12.5 + 12.5

= 25 in.

Answer:

[tex](f - g)(x) = {x}^{3} - 6 {x}^{2} + 18x - 10[/tex]

Step-by-step explanation:

The given functions are:

[tex]f(x) = {x}^{3} - 2 {x}^{2} + 12x - 6[/tex]

and

[tex]g(x) = 4 {x}^{2} - 6x + 4[/tex]

We want to find

[tex](f - g)(x)[/tex]

Recall that:

[tex](f - g)(x) = f(x) - g(x)[/tex]

This implies that:

[tex](f - g)(x) = {x}^{3} - 2 {x}^{2} + 12x - 6 - (4 {x}^{2} - 6x + 4)[/tex]

[tex](f - g)(x) = {x}^{3} - 2 {x}^{2} + 12x - 6 - 4 {x}^{2} + 6x - 4[/tex]

We combine similar terms to get:

[tex](f - g)(x) = {x}^{3} - 6 {x}^{2} + 18x - 10[/tex]

Answer:

Solution given:

f(x)=x3−2x2+12x−6

g(x)=4x2−6x+4

now

(f-g)(x)=f(x)-f(g)=x3−2x2+12x−6-4x²+6x-4

=x³-6x²+18x-10

Answer: A cereal with 0 grams of sugar has a rating of about 57

Step-by-step explanation:

The equation modelling the taste rating of a cereal, y, in a survey, where x is the number of grams of sugar per serving is expressed as

yˆ=2.391x + 57.420

This is a straight line graph represented in the slope intercept form which is expressed as

y = mx + c

Where

m represents the slope of the straight line

c represents the y intercept. The y intercept is the point at which x = 0.

From the given equation, the y intercept is 57.420

It means that a cereal with 0 grams of sugar has a rating of about 57

Final answer:

The child's shadow is lengthening at a rate of 6 m/min as they walk away from the street lamp.

Explanation:

The child's shadow lengthens as they walk away from the street lamp because the angle between the child and the light source increases. To find the rate at which the shadow lengthens, we can use similar triangles. The ratio of the length of the shadow to the height of the child remains constant. So, if the child's height increases by 1 meter, the shadow length increases by 6 meters. Therefore, the child's shadow is lengthening at a rate of 6 m/min.

The rate of lengthening of the child's shadow is 4 meters per minute.

Step 1: Defining the variables.

Let:

It is given that the child walks away from the light at a rate of 20 m/min. This is:

[tex]\frac{dx}{dt} = 20\ meters\ per\ min[/tex]

Step 2: Relating the variables using similar triangles.

The two triangles formed (one by the lamp post and its shadow, and the other by the child and the child's shadow) are similar. Therefore, the following proportion:

[tex]\frac{x+s}{h} = \frac{s}{y}[/tex]

Substituting the known values (h = 6 m and y = 1 m), we get:

[tex]\frac{x+s}{6} = \frac{s}{1}[/tex]

Step 3: Solving for s.

Cross-multiplying gives:

[tex]6s=x+s[/tex]

Rearranging terms:

[tex]5s=x[/tex]

So the length of the shadow, s, in terms of the child's distance from the lamp, x, is:

[tex]s = \frac{x}{5}[/tex]

Step 4: Differentiate with respect to time.

Differentiating both sides with respect to t:

[tex]\frac{ds}{dt} = \frac{1}{5}\frac{dx}{dt}[/tex]

Substituting the known rate of change [tex]\frac{dx}{dt} = 20\ meters\ per\ min[/tex]:

[tex]\frac{ds}{dt} = \frac{1}{5}*20 = 4\ meters\ per\ min[/tex]

Therefore, the child's shadow is lengthening at a rate of 4 meters per min.

Final answer:

The median is a more accurate indicator of the average student's SAT score at Groveland High School in a right-skewed distribution because it is not affected by outliers, unlike the mean.

Explanation:

The question addresses why the median is a more accurate indicator of the SAT score of the average student at Groveland High School rather than the mean when the data is strongly skewed to the right. This is because the median is the middle value that divides the number set into two equal halves, and it is not affected by outliers or extremely high scores that are present in a right-skewed distribution. In contrast, the mean is the average of all values and can be significantly influenced by outliers, leading to a value that may not accurately represent the 'central' tendency of the data. Thus, for a right-skewed data set, the median provides a better measure of center for what can be considered a typical score because it is not skewed by unusually high values.

The outward pressure created by nuclear fusion within the core of stars, like the Sun, counteracts the force of gravity, preventing them from collapsing under their own self-gravity. This delicate balance sustains the stability and longevity of stars.

The correct answer is D. The outward pressure created by nuclear fusion.

Explanation: Stars, including the Sun, are massive celestial objects formed primarily of hydrogen and helium gas. In their cores, the extreme temperatures and pressures enable nuclear fusion reactions to occur, converting hydrogen into helium and releasing tremendous amounts of energy. This energy generates an outward pressure that counteracts the inward force of gravity, maintaining the star's equilibrium and preventing it from collapsing under its own self-gravity. This balance between gravitational forces pulling inward and outward pressure pushing outward due to nuclear fusion is what keeps stars, like the Sun, stable and prevents them from collapsing.

I believe the answer is B. Hope this helps!

Answer:

2,880 tons of sand

Step-by-step explanation:

In this question, we are asked to calculate the amount of tons of sand required to produce a certain amount of tarry materials if a certain amount of sand had produce an amount of tarry materials.

We work as follows:

First, we write the relation that 144,000 tons of sand produces 125,000 barrels of tarry material, then x of tons would produce 2,500 barrels of tarry materials

To find c, we cross multiply:

x * 125,000 = 2,500 * 144,000

x = (2,500 * 144,000)/125,000

x = 2,880

Answer: 360 mg of the medicine will be detected after 48 hours

Step-by-step explanation:

We would apply the formula for exponential decay which is expressed as

A = P(1 - r)^t

Where

P represents the initial dosage of the medicine.

A represents the final dosage of the medicine after t hours.

t represents the number of hours.

r represents the rate of decay

From the information given

P = 1000 mg

r = 40% = 40/100 = 0.4

The expression becomes

A = 1000(1 - 0.4)^t

A = 1000(0.6)^t

In 48 hours, t = 2

Therefore,

A = 1000(0.6)^2

A = 360

Answer:

130°

Step-by-step explanation:

The diagram for the question is redrawn on the attached image. It was obtained online.

Basically, what the question is asking is for the angle between the new path of the beam and the old path if the beam continued without being reflected by the mirror.

The line of the old path of the beam of light is a straight line. And the sum of angles on straight line = 180°

25° + 25° + y° = 180°

y = 180° - 50° = 130°

Answer:

[tex]\\3 percent of 900 = 27 \\900 + 27 = 927 \\ 927 * 36 = 33372[/tex]

Step-by-step explanation:

First you have to find out the 3% of 900 (is 27)

then you add 27 to 900

then you multiply it by 3 years (36 months)

and your result is 33372 :)

The rent over the three-year term of the new lease will be $33,372, calculated with a 3% increase annually.

Step 1:

Calculate the new monthly rent after the 3% increase.

The new monthly rent will be the current rent plus 3% of the current rent.

New monthly rent = $900 + 0.03 * $900 = $900 + $27 = $927.

Step 2:

Calculate the total rent over the three-year term.

Since there are 12 months in a year and the lease is for three years, multiply the new monthly rent by the number of months in three years.

Total rent over three years = $927/month * 12 months/year * 3 years = $33,372.

So, the rent over the three-year life of the new lease will be $33,372.

Answer:

The constant of variation, k = 0.57

Step-by-step explanation:

We are given that z varies jointly as the second power of x (x²), and the third power of y (y³).

For a constant of variation, k, z can be written as

z = x²y³k.

We are also given

z = 31.5

x = 2

x = 2.4

31.5 = (2²)(2.4)³k

31.5 = 4×13.824k

31.5 = 55.296k

k = 31.5/55.296

= 0.57

Answer:

Step-by-step explanation:

Let x represent the constant amount by which the length and width of the garden is increased.

Tyler has a rectangular garden that measures 10 m wide by 13 m long. He wants to increase the area to 208 m² by increasing the width and length by the same amount. This means that the new length of the garden would be (13 + 2x) cm and the new width of the garden would be (10 + 2x) cm. Therefore,

(13 + 2x)(10 + 2x) = 208

130 + 26x + 20x + 4x² -208 = 0

4x² + 46x - 208 - 130 = 0

4x² + 46x - 78 = 0

Dividing through by 2, it becomes

2x² + 23x - 39 = 0

2x² + 26x - 3x - 39 = 0

2x(x + 13) - 3(x + 13) = 0

2x - 3 = 0 or x + 13 = 0

x = 3/2 or x = - 13

Since the value of x cannot be negative, then

x = 3/2 = 1.5 m

The length of the new garden is

13 + 1.5 = 14.5 m

Answer:

C) 52 in^3

Step-by-step explanation:

The first is to determine the formula of the volume of the box, which would be the following:

 V = height * length * width

Knowing that we have a rectangular piece we will determine the maximum volume, we will double a distance x (which will be the height) in the width and length of the piece, therefore as it is on both sides, the length and width are defined from the Following way:

length = 10 - 2 * x

width = 8 - 2 * x

height = x

Now we calculate the volume:

V = x * (10-2 * x) * (8-2 * x)

To determine the maximum volume we will give values to x in order to see how it behaves:

Let x = 2.5

V = (5) * (3) * (2.5) = 37.5

Let x = 2

V = (6) * (4) * (2) = 48

Let x = 1.5

V = (7) * (5) * (1.5) = 52.5

Let x = 1

V = (8) * (6) * (1) = 48

Let x = 0.5

V = (9) * (7) * (0.5) = 31.5

It can be seen that the greatest volume is obtained when the height is equal to 1.5 and its volume is 52.5 in ^ 3

Answer:

Mixed mode expression

Step-by-step explanation:

Mixed mode expression is an expression that contains or have operands that have different data types.

In this case, she has to generate values that have type equal to the operands in this situation.

Answer:

The answer to this question is N(0.50,0.091), just took a quiz with same question.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Relatively less golf and attend relatively more concerts whenever his leisure time becomes more scarce.

- This is called the marginal utility, that with every successive unit that utility decreases. With each passing hour while playing golf Joe is less inclined to play for an extra hour. When leisure time is less than 2 hrs he is equally likely to opt out of golf for concert.

Answer:

7

Step-by-step explanation:

(x+3)/(x+8) = 2/3

3x + 9 = 2x + 16

x = 7