What is the minimum number of cards that must be drawn from an ordinary deck of cards to guarantee that you have been dealt at least three aces?

Answer:

[tex]\sin\left(x+\frac{\pi}{7} \right)[/tex]

Step-by-step explanation:

[tex]\sin\left(x+\frac{\pi}{7} \right)=\sin \frac{\pi}{7}\cos x +\cos \frac{\pi}{7} \sin x[/tex]

the ratio of the area of square KLMN to the area of LOK is 2a^2/b h

From the image given, we can deduce the following;

The formula for area of a square is

Area = a^2

Where, 'a' is the side

The formula for area of a triangle

Area = 1/ 2 base × height

Now, let's find the ratio

Ratio = area of KLMN/ area of LOK

Ratio = [tex]\frac{a^2}{\frac{1}{2} bh}[/tex]

Ratio = [tex]\frac{a^2}{\frac{bh}{2} }[/tex]

make the expression linear

Ratio = 2a^2/bh

The ratio of  the area of square KLMN to the area of LOK is 2a^2/bh

Thus, the ratio of the area of square KLMN to the area of LOK is 2a^2/b h

Learn more about area here:

https://brainly.com/question/25260313

#SPJ1

The equation which can be used to find the length of EF is option A which is  EF=[tex]\sqrt{24^{2} -12^{2} }[/tex].

Given the length of base of right angled triangle is 12 and the hypotenuse be 24.

We are to find the length of EF and tell which equation can be used to find the length of EF.

We know that pythagoras theorem applies in a right angled triangle.

Pythagoras theorem says that in a right angled triangle the square of the hypotenuse is equal to the sum of square of base and perpendicular.

[tex]H^{2} =B^{2} +P^{2}[/tex]

In this triangle we are only given base and hypotenuse and we have to find EF which is perpendicular.

[tex](DE)^{2} =(EF)^{2} +(DF)^{2}[/tex]

EF=[tex]\sqrt{DE^{2}-DF^{2} }[/tex]

=[tex]\sqrt{(24)^{2} -(12)^{2} }[/tex]--1

=[tex]\sqrt{576-144}[/tex]

=[tex]\sqrt{432}[/tex]

Hence the equation which can be used to find the length of Ef is option A which is  EF=[tex]\sqrt{24^{2} -12^{2} }[/tex].

Question is incomplete as it should include the figure also.

Learn more about pythagoras theorem at https://brainly.com/question/343682

#SPJ1

Answer:

$7.14

Step-by-step explanation:

Given:

Isabel , Nancy = 2 humans

Bill = $12.42

Tip = 15%

To Find:

How much will each girl pay if they equally divide the total amount?

Solve:

$12.42 × 15% = 1.863

1.863 ≈ 1.86

$12.42 + 1.86 = 14.28

14.28 ÷ 2 = 7.14

Therefore each girl pays $7.14 .

~Kavinsky

Answer:

when x=-7

Step-by-step explanation:

if u are solving a function like this, u must not have a division by zero so if we put x=-7 in the function we hav a division by zero

The value of x in the angles of Quadrilateral is 52 degree.

According to the statement

we have given a four angles and we have to  find the value of x in these give angles.

From given 4 angles it is clear that the these angles are of a quadrilateral.

And we know that the

A quadrilateral is a four-sided polygon, having four edges and four corners.

And the sum of all angles of a quadrilateral is 360 degree.

so,

50° + 3X + X + (X+110) = 360 degree

50° + 4X + (X+110) = 360 degree​

50° + 5X + 110 = 360 degree

160° + 5X  = 360

5X = 360-100

5X = 260

X = 52 degree.

So, The value of x in the angles of Quadrilateral is 52 degree.

Learn more about Quadrilateral here

https://brainly.com/question/16691874

#SPJ1

The transformations that would be used on the blue segment CD to get it to match with the red segment C2D2 is to effect a 180° clockwise rotation, so that C remains at (3, -10) and D assumes (3, -11). Recall that original coordinates were: C (3, -10); D (5, -10).

A transformation is a broad phrase covering four distinct methods of changing the shape and/or location of a point, line, or geometric figure.

The pre-Image is the original shape of the item, and the Image during the transformation is the final shape and location of the object. The following are different types of transformation in math:

The type of transformation that will be used here is called reflection.

D retains it's original coordinates of (5, -10); E goes to (6, -11) and F (6, -10).

The line with the coordinates [(4, -11) and (4, -10) that is EF is parallel to [(3,-11) and (3, -10).

Parallel lines are lines that are always the same width apart in a plane. Parallel lines never cross.

The lines that are perpendicular are: AB with coordinates A(3, -9) & B(3, -11) and CD with coordinates (3, -10) and (5, -10). Lines that intersect each other forming a right angle are called perpendicular lines.

The line segments on the boat that have a slope of zero are:
EF, AB AC, BC.  A line with zero slope is one that has a constant value shown along the y-axis that does not vary over the line's points.

The line segments on the boat that are undefined are:
CD, CF, and DF. The gradient or slope of any vertical line that travels up or down is the undefined slope.

The slope (m) is calculated as:
(Y2-Y1)/(X2 - X1)

Given that:

Y1 = 5

Y2 = 4

X1 = -10

X2 = -11

Hence,
m = (5-4)/(-11 -10)

m = -0.048

Learn more about Transformation:
https://brainly.com/question/1548871
#SPJ1

we are given x here, so we already know that our first coordinate is equal to -2.

in order to find the next coordinate, we have to substitute x for -2 in the y=mx+b equation.

the equation is

[tex]y = \frac{2}{3} x + 23[/tex]

so in substituting x for -2 we get

[tex]y = \frac{2}{3} ( - 2) + 23[/tex]

all we need to do is multiply ⅔ by -2, which gives us -1,3333.

we now have

[tex]y = - 1.3333 + 3[/tex]

so we add them together and get :

[tex]y = 1.666666[/tex]

hope this helps!!<3

Total number of men and women wearing sunglasses = 290

According to the question,

Total number of men and women = 2000

half of the adults were women = 1/2 × 2000

Number of women = 1000

Number of men = (Total adults) - (Number of women )

Number of men = 2000 - 1000

= 1000

given,

20% of women were wearing sunglasses = 20/100 × 1000

= 200

9% of men were wearing sunglasses = 9/100 × 1000

= 90

Total number of adults wearing glasses = 200 + 90

= 290

In mathematics, a percentage is a number or ratio that represents a fraction of 100. It is often denoted by the symbol "%" or simply as "percent" or "pct." For example, 35% is equivalent to the decimal 0.35, or the fraction.

To learn more about percentage from the given link

https://brainly.com/question/24304697

#SPJ4

Answer:

$1118.88

Step-by-step explanation:

Lets start by finding all sides of the perimeter to get an accurate measure of the area.

We know the width is 14.8 feet, that means the opposite side also equals 14.8 feet.

Now the other two sides must sum to 50.4 (80-(14.8*2)) and be equal, so we can divide 50.4 by two to get 25.2 for the other two sides.

Now we can calculate area by multiplying one from each side:

[tex]14.8*50.4=745.92[/tex]

Now to find the price of required sod, multiply the area by cost per square foot

[tex]745.92*1.50=1118.88[/tex]

Therefore it will cost 1118.88 dollars to cover the entire area in sod.

Answer:

$1.77 per pound

Step-by-step explanation:

To find the unit price we divide the cost over the weight: 123.99/70 = 1.77128571 = 1.77

The maximum possible side length of the base of the building is; C: 71 feet.

The given parameters of the new building in the shape of a square pyramid that is to be constructed are as follows:

Base is expressed as b

Slant height (l) is expressed as 5b

The lateral surface area of the square pyramid is calculated from the formula given as;

LSA = 2bl

Thus, the lateral surface area is expressed as;

L = 2 * b * 5b

L = 10b²

The total surface area is calculated using the formula:

T = L + b²

Thus, plugging in the value of 10b² for L gives the total surface area as;

T = 10b² + b²

T = 11b²

The maximum surface area is 50,000 square feet and so we can find b from the following expression;

11b² = 50000

Divide both sides of the equation by 11 to get;

b² = 50000/11

b = √(50000/11)

b =  71 feet to the nearest foot.

Read more about Pyramid side length at; https://brainly.com/question/22744289

#SPJ1

Answer:

Step-by-step explanation:

Answer: 10xy-12+15x-8y=(5x-4)*(2y+3).

Step-by-step explanation:

[tex]10xy-12+15x-8y=(10xy-8y)+(15x-12)=\\=2y*(5x-4)+3*(5x-4)=(5x-4)*(2y+3).[/tex]

Answer:

x < 1/2

Step-by-step explanation:

2(1-x) > 2x

2-2x > 2x

2 > 4x

1/2 > x

Answer:

x<1/2

Step By Step Explanation

Let's solve your inequality step-by-step.

2(1−x)>2x

Step 1: Simplify both sides of the inequality.

−2x+2>2x

Step 2: Subtract 2x from both sides.

−2x+2−2x>2x−2x

−4x+2>0

Step 3: Subtract 2 from both sides.

−4x+2−2>0−2

−4x>−2

Step 4: Divide both sides by -4.

-4x/2>-2/4

x<1/2

The standard deviation of the x distribution is 0.2.

According to the statement

we have given that the the sample n is 64 and we have to find the standard deviation of the given sample.

So, For this purpose, we know that the

The standard deviation of the sample is the standard deviation of population divided by the square root of the length of the sample.

In this problem, we have that the value of alpha is

[tex]\alpha = 1.6[/tex]

Suppose that for aluminum alloy sheets of a particular type,

If X is the sample mean Young's modulus for a random sample of n = 64 sheets, and the standard deviation of the X distribution is given by

[tex]s = \frac{\alpha}{\sqrt{64} }[/tex]

then solve it then the standard deviation

s =  {1.6} / {8 }

s = 0.2

So, The standard deviation of the x distribution is 0.2.

Disclaimer: This question was incomplete. Please find the full content below.

Question:

Given that Young's modulus is a quantitative measure of stiffness of an elastic material. Suppose that for aluminum alloy sheets of a particular type, its mean value and standard deviation are 70 GPa and 1.6 GPa, respectively.

a. If X is the sample mean Young's modulus for a random sample of n = 64 sheets, the sampling distribution of X centered at 70 GPa, and the standard deviation of the X distribution is given by

Learn more about Standard deviation here

https://brainly.com/question/475676

#SPJ4

Answer:

Step-by-step explanation:

The vertical distance between the given points is:

Answer:

19,497m

Step-by-step explanation:

8,856-(-10,911)

=8856+10,911

=19,497m

Answer:

17 hours

Step-by-step explanation:

We first want to figure out how much money shes making per hour.

We can simply divide 176 by 8 getting us 22

Since we know she makes 22 dollars an hour we can divide 374 by 22 getting us 17.

Now we know it would take 17 hours to make 374 dollars

If you want to double check you can simply multiply 17 by 22 which would get you 374

Answer: 17 hours

Step-by-step explanation

It looks like the limit is

[tex]\displaystyle \lim_{x\to0} \frac{e^{3x} - 1 - 3x}{x^2}[/tex]

L'Hôpital's rule works in this case; applying it twice gives

[tex]\displaystyle \lim_{x\to0} \frac{e^{3x} - 1 - 3x}{x^2} = \lim_{x\to0} \frac{3e^{3x} - 3}{2x} = \lim_{x\to0} \frac{9e^{3x}}{2} = \boxed{\frac92}[/tex]

Answer:

The number is 72.

Step-by-step explanation:

Let the number be xy.

x = y + 5

10x + y - 2(10y + x) = 0.25(10x + y)

10x - 2x + y - 20y = 2.5x + 0.25y

5.5x - 19.25y = 0

Substituting for x:

5.5y + 27.5  - 19.25y = 0

-13.75y = -27.5

y = 2.

So x = 2 + 5 = 7.

Answer:

Separating the 3x and -5 apart from the (x+1)

Step-by-step explanation:

It would turn out to be (3x-5)(x+1) !

Factor out x+1 from the expression

(x+1) x (3x-5)

Answer:

=========================

Triangle with:

As per definition of midsegment, it is connecting the midpoints of two sides and its length is half the length of the opposite side of the triangle.

So we have:

Solve it for n:

Correct choice is D.

Considering the situation described, the classification of the runners is given as follows:

Dan - Ben - Alex - Curtis.

The oldest came in second place. Ben is older than Alex, and Curtis is older than Dan, hence either Ben or Curtis finished second.

Alex ran the distance faster than Curtis, and Dan ran faster than Ben and Curtis, hence considering the above observation Ben finished second and the classification is:

Dan - Ben - Alex - Curtis.

A similar problem, in which a situation is interpreted, is given at brainly.com/question/5660603

#SPJ1

To acquire 90000000 views on his channel, he has to upload 20 videos every month.

Every month, he  posts 3 videos to his  channel. An average number of people watch each video. = 1500000

In search of:

How many months must pass before he begins to receive 90,000,000 views on his channel?

Step 1

On his channel, he posts three videos each month.

The average number of views per video is.

3 Videos Receive Views

= 3 * 1500000

= 4,500,000 Views

Number of 4,500,000 views each month

Complete 90000000 Views

Step 2

Total Views/Months = Total Views/Total Views

Days in a month = 90000000/4500000

                             = 20

20 Monthly months in the number

To acquire 90000000 views on his channel, he has to upload 20 videos every month.

20  Months is the right response, so.

To know more about Average number's visit:

https://brainly.com/question/16956746

#SPJ4

Step-by-step explanation:

the midpoint is exactly halfway in each coordinate direction.

so, whatever we have to add ti or subtract from the coordinates of T to get to the midpoint, we have to add to or subtract from the midpoint to get to S.

for x we get

0 + 5 = 5

so, we need to add another 5 to get the x coordinate of S.

that is then 5 + 5 = 10

for y we get

2 - 5 = -3

so, we need to subtract another 5 to get the y coordinate of S.

that is then

-3 - 5 = -8

S = (10, -8)

Answer:

A = (0, b)

B = (a, b)

Step-by-step explanation:

A is straight up from the origin and is the same height as b so it's (0, b)

B is straight up from C so the x is the same so it's (a, b)

The term that is not possible in the domain of a sequence is:

-5.

The domain of a function is the set that contains all possible input values for the function. For a sequence, the domain is the set that contains all the indexes of the terms, starting at 0 and going until the nth term.

For example, suppose we have the following sequence: 3, 5, 7, ...

From what was explained above, which also can be visualized with the example, an index term of a sequence cannot be negative, hence the term that is not possible in the domain of a sequence is:

-5.

Which is the only negative number of the options.

More can be learned about the domain of a function at brainly.com/question/10891721

#SPJ1

Based on the calculations, the measure of angle BDF and CFG are 100° and 38° respectively.

In Geometry, two (2) straight lines are considered to be parallel if their slopes are the same (equal) and they have different y-intercepts. This ultimately implies that, two (2) straight lines are parallel under the following conditions:

m₁ = m₂

Note: m is the slope.

The alternate interior angles theorem states that when two (2) parallel lines are cut through by a transversal, the alternate interior angles that are formed are congruent.

Based on the alternate interior angles theorem, we can infer and logically deduce the following properties from the diagram (see attachment):

For angle BDF, we have:

<BDF = <BDH + <HDF

<BDF = 38° + 62°

<BDF = 100°.

Since angles BDF and DFC are linear pair, they are supplementary angles. Thus, we have:

∠BDF + <DFC = 180°

<DFC = 180 - ∠BDF

<DFC = 180 - 100

<DFC = 80°.

For angle CFG, we have:

∠DFE + <DFC + <CFG= 180°

<CFG = 180° - ∠DFE - <DFC

<CFG = 180° - 62° - 80°

<CFG = 38°.

Read more on parallel lines here: https://brainly.com/question/3851016

#SPJ1

The volume of the tank is (70 cm)³ = 343,000 cm³.

Now,

1 mL = 1 cm³

1 L = 1000 mL

so we convert the given rate to

[tex]\dfrac{7\,\rm L}{1\,\rm min} \cdot \dfrac{1000\,\rm mL}{1\,\rm L} \cdot \dfrac{1\,\mathrm{cm}^3}{1\,\rm mL} = \dfrac{7000\,\mathrm{cm}^3}{1\,\rm min}[/tex]

Then the time it will take to fill up the tank is

[tex]343,000\,\mathrm{cm}^3 \cdot \dfrac{1\,\rm min}{7000\,\mathrm{cm}^3} = \boxed{49\,\rm min}[/tex]