PLEASE HELP ME WITH THIS MATH QUESTION

Answer:

a) The probability of being dealt a blackjack hand

[tex]= \frac{64}{1326}[/tex]

b) Approximate percentage of hands winning blackjack​ hands

[tex]4.827%[/tex]

Step-by-step explanation:

It is given that -

Winning Black Jack means -  getting 1 of the 4 aces and 1 of 16 other cards worth 10 points

Thus, in order to win a "black jack" , one is required to pull 1 ace and 1 of 16 other cards

Number of ways in which an ace card can be drawn from a set of 4 ace card is [tex]C^4_1[/tex]

Number of ways in which one card can be drawn from a set of other 16 card is [tex]C^16_1[/tex]

Number of ways in which two cards are drawn from a set of 52 cards is [tex]C^52_2[/tex]

probability of being dealt a blackjack hand

[tex]= \frac{C^4_1* C^16_1}{C^52_2} \\= \frac{4*16}{\frac{51*52}{2} }\\ = \frac{64}{1326} \\[/tex]

Approximate percentage of hands  winning blackjack​ hands

[tex]= \frac{64}{1326} * 100\\= 4.827[/tex]%

After completing this question, I got the calculation that the probability of being dealt a blackjack hand is 32/663. The percentage is 4.83%, or as a decimal ~0.0483

Answer:

  C, D, B, A

Step-by-step explanation:

The greater the angle the tangent line makes with the positive x-axis, the greater the slope. Angles increase in the counterclockwise direction, so the question here is equivalent to asking for the tangent lines to be put in clockwise (decreasing slope) order.

That order is C, D, B, A.

Answer:

  D.)  AB≅A′B′, ∠A≅∠A′, and ∠C≅∠C′

Step-by-step explanation:

Option A identifies two sides and the angle not between them. The two triangles will be congruent in that case only if the angle is opposite the longest side, which is not true in general.

Option B: same deal as Option A.

Option C identifies three congruent angles, which will prove the triangles similar, but not necessarily congruent.

Option D identifies two angles (sufficient for similarity) and one side, sufficient (with similarity) for congruence. The applicable congruence theorem is AAS.

The statements that could be used to prove that ΔABC and ΔA′B′C′ are congruent are: A.) ∠A≅∠A′, AC≅A′C′, and BC≅B′C′; C.) ∠A≅∠A′, ∠B≅∠B′, and ∠C≅∠C′; and D.) AB≅A′B′, ∠A≅∠A′, and ∠C≅∠C′.

The statements that could be used to prove that ΔABC and ΔA′B′C′ are congruent are:

A.) ∠A≅∠A′, AC≅A′C′, and BC≅B′C′

C.) ∠A≅∠A′, ∠B≅∠B′, and ∠C≅∠C′

D.) AB≅A′B′, ∠A≅∠A′, and ∠C≅∠C′

In order for two triangles to be congruent, their corresponding angles and sides need to be congruent. In this case, option A states that ∠A≅∠A′, AC≅A′C′, and BC≅B′C′, which satisfies the conditions for congruence. Option C has congruent angles but does not mention congruent sides, so it does not prove congruence. Option D mentions congruent sides but does not mention congruent angles, so it also does not prove congruence.

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Answer:

  8184 vocalists sang in total

Step-by-step explanation:

The number needed is ...

  8 + 16 + 32 + 64 + 128 + 256 + 512 + 1024 + 2048 + 4096

You can add these up to get a total of 8184, or you can use the formula for the sum of a geometric series:

  Sn = a1(r^n -1)/(r -1) . . . . where a1 is the first term and r is the common ratio

  S10 = 8(2^10 -1)/(2 -1) = 8(1024 -1)/1 = 8184

Answer:

6,138

Step-by-step explanation:

Number of vocalist needed on the first day = 6

Each day after that, the number of vocalists needed doubles

To Find:

The total number of vocalist found on the 10th day = ?

Solution:

By using the geometric series

Where

a is the first term

r is the ratio

n is the number of terms

On substituting the values

That is

The first day = 6 vocalist

Second day = 12 vocalist

third day =24 vocalist

Fourth day   =48 vocal list

Fifth day = 96 vocalist

Sixth day = 192 vocalist

Seventh day = 384 vocalist

eight day = 768 vocalist

Ninth day = 1536 vocalist

Tenth day = 3072 vocalist

So

6+12+24+48+96+192+384+768+1536+3072 = 6138 vocalist sang in total on the  end of tenth day.

Answer:

let the equal sides of the triangle be of length "a"  . let the angle between these two sides be " x  ". Then drop a perpendicular from the vertex to the base.  now u have 2 similar triangles  .the angle between the perpendicular and one of the equal sides is now (x/2)  . length of perpendicular = a cos(x/2)  length of base = 2a sin(x/2)  . area of triangle = (1/2) 2sin(x/2) cos(x/2) a-square  

= (1/2) (sin x) a-square

Answer:

7 rpm = 0.73 rad/s

Step-by-step explanation:

R = Radius of merry-go-round = 1.8 m

[tex]I_M[/tex]= Moment of inertia of merry-go-round = 255 kg m²

[tex]I_C[/tex]= Moment of inertia of child

ω = 9 rev/min

m = Mass of child = 24 kg

From the conservation of angular momentum

[tex]I\omega=I'\omega '\\\Rightarrow I\omega=(I_M+I_C)\omega'\\\Rightarrow \omega'= \frac{I\omega}{(I_M+I_C)}\\\Rightarrow \omega'=\frac{I\omega}{(I_M+mR^2)}\\\Rightarrow \omega'=\frac{255\times 9}{(255+24\times 1.8^2)}\\\Rightarrow \omega'=6.9\ rev/min[/tex]

∴ New angular speed of the merry-go-round is 7 rpm = [tex]7\times \frac{2\pi}{60}=\mathbf{0.73\ rad/s}[/tex]

Answer:

Converges to -25.

Step-by-step explanation:

[tex]\sum_{k=1}^{\infty} -5 \cdot (\frac{4}{5})^{k-1}[/tex] converges since [tex]r=\frac{4}{5}<1[/tex].

The sum is given by [tex]\frac{a_1}{1-r}[/tex] where [tex]a_1[/tex] is -5.

[tex]\frac{-5}{1-\frac{4}{5}}=\frac{-5}{\frac{1}{5}}=-5(5)=-25[/tex].

For this case we have the following expression:

[tex]\sqrt [3] {5x-2} - \sqrt [3] {4x} = 0[/tex]

If we add to both sides of the equation [tex]\sqrt [3] {4x}[/tex] we have:

[tex]\sqrt [3] {5x-2} = \sqrt [3] {4x}[/tex]

To eliminate the roots we must raise both sides to the cube:

[tex](\sqrt [3] {5x-2}) ^ 3 = (\sqrt [3] {4x}) ^ 3\\5x-2 = 4x[/tex]

So, the correct option is the option c

Answer:

Option C

Answer:

C

Step-by-step explanation:

[tex]\bf \textit{Sum and Difference Identities} \\\\ tan(\alpha + \beta) = \cfrac{tan(\alpha)+ tan(\beta)}{1- tan(\alpha)tan(\beta)} \qquad tan(\alpha - \beta) = \cfrac{tan(\alpha)- tan(\beta)}{1+ tan(\alpha)tan(\beta)} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ tan(x-3\pi )=\cfrac{tan(x)-tan(3\pi )}{1+tan(x)tan(3\pi )} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf tan(3\pi )\implies \cfrac{sin(3\pi )}{cos(3\pi )}\implies \cfrac{0}{-1}\implies 0\qquad therefore \\\\[-0.35em] ~\dotfill\\\\ tan(3\pi )=\cfrac{tan(x)-tan(3\pi )}{1+tan(x)tan(3\pi )}\implies tan(x-3\pi )=\cfrac{tan(x)-0}{1+0} \\\\\\ tan(x-3\pi )=\cfrac{tan(x)}{1}\implies tan(x-3\pi )=tan(x)[/tex]

Answer:

7

Step-by-step explanation:

I am assuming that the division problem looks like this:

-2|  1   2   -3   1

Going off that assumption, we will work this problem.  The first thing you always do in the execution of synthetic division is to bring down the first number.  Then multiply that number by the one "outside", which is -2, then put that number up under the next number in the line:

-2|  1   2   -3   1

         -2

     1

Now add the 2 and -2 and bring that down as a 0 and multiply the -2 times the 0:

-2|   1   2   -3   1

          -2    0

      1    0

Now add -3 and 0 to get -3 and multiply that -3 times the -2 and put the product up under the next numbe in line;

-2|   1   2   -3   1

           -2   0  6

      1     0   -3

Now add the 1 and the 6 to get the remainder:

7

Answer: 7

Step-by-step explanation:

A

P

E

X

By the conditional property we have:

If A and B are two events then A and B are independent if:

                  [tex]P(A|B)=P(A)[/tex]

                               or

                 [tex]P(B|A)=P(B)[/tex]

( since,

if two events A and B are independent then,

[tex]P(A\bigcap B)=P(A)\times P(B)[/tex]

Now we know that:

[tex]P(A|B)=\dfrac{P(A\bigcap B)}{P(B)}[/tex]

Hence,

[tex]P(A|B)=\dfrac{P(A)\times P(B)}{P(B)}\\\\i.e.\\\\P(A|B)=P(A)[/tex] )

Based on the diagram that is given to us we observe that:

Region A covers two parts of the total area.

Hence, Area of Region A= 72/2=36

Hence, we have:

[tex]P(A)=\dfrac{36}{72}\\\\i.e.\\\\P(A)=\dfrac{1}{2}[/tex]

Also,

Region B covers two parts of the total area.

Hence, Area of Region B= 72/2=36

Hence, we have:

[tex]P(B)=\dfrac{36}{72}\\\\i.e.\\\\P(B)=\dfrac{1}{2}[/tex]

and A∩B covers one part of the total area.

i.e.

Area of A∩B=74/4=18

Hence, we have:

[tex]P(A\bigcap B)=\dfrac{18}{72}\\\\i.e.\\\\P(A\bigcap B)=\dfrac{1}{4}[/tex]

Hence, we have:

[tex]P(A|B)=\dfrac{\dfrac{1}{4}}{\dfrac{1}{2}}\\\\i.e.\\\\P(A|B)=\dfrac{2}{4}\\\\i.e.\\\\P(A|B)=\dfrac{1}{2}[/tex]

Hence, we have:

[tex]P(A|B)=P(A)[/tex]

         Similarly we will have:

[tex]P(B|A)=P(B)[/tex]

Answer:

  3/10

Step-by-step explanation:

Bonnie has completed 0.5 + 0.2 = 0.7 of her art project. 1 - 0.7 = 0.3 of her art project remains to be completed.

_____

1/2 = 5/10 = 0.5

1/5 = 2/10 = 0.2

An exponential function may be given by:

f(x) = A(1+r)^x

A is the initial amount and r is a decimal representing the growth rate.

We can see that 1+r = 1.2, and we solve for r:

1 + r = 1.2

r = 0.2

The growth rate is 0.2, or 20%

Choice B

The rate of growth of Mason's daily sales is 20%.

The rate of growth of Mason's daily sales can be found by determining the percentage increase in the sales from one day to the next. To find this, we can compare the sales on two consecutive days and calculate the ratio of the second day's sales to the first day's sales. Let's consider the sales on the first day (x) and the sales on the second day (x+1).

Given the sales model f(x) = 50(1.2)^x, we can substitute x and x+1 into the equation to get the sales on the first and second day, respectively. The ratio of the second day's sales to the first day's sales is:

f(x+1) / f(x) = (50(1.2)^(x+1)) / (50(1.2)^x) = 1.2.

So, the rate of growth is 1.2, which represents a 20% increase in sales from one day to the next.

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Answer:

The range in shelter A is 22, and the range in shelter B is 18.

Step-by-step explanation:

The range is the largest value minus the smallest value.

For shelter A, the range is 30 − 8 = 22.

For shelter B, the range is 28 − 10 = 18.

Answer:

The range in shelter A is 22, and the range in shelter B is 18.

Step-by-step explanation:

The box plots show the weights, in pounds, of the dogs in two different animal shelters. The range in shelter A is 22, and the range in shelter B is 18 correctly compares the ranges of the data.

Answer:

The first option:

Vertices: A, B, C, D, E, F, G, H;

Edges: AB, BC, CD, DA, BE, EF, FG, GH, HE, AH, CF, and DG;

Bases: rectangle ABEH and rectangle DCFG

Hope this helps C:

The correct option is option A:

    rectangular prism

The point where 2 or more side intersects is called vertices.

The individual flat surface of the solid object is the face.

The line segment where 2 faces intersect each other.

The prism whose bases are rectangular and are connected by line segment is called a rectangular prism.

As Rectangular prism has 2 rectangular bases at top and bottom position of the prism, 8 vertices, 6 faces, and 12 sides.

From the definition, It is clear that,

This figure is a rectangular prism whose

8 vertices are: A, B, C, D, E, F, H, G.

12 edges are: AB, BC, CD, DA, BE, EF, FG, GH, HE, AH, CF, and DG

2 rectangular bases are: ABEH and DCFG

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[tex]

A(4,-2) \\

B(0, 10) \\

AB=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\

AB=\sqrt{(0-4)^2+(10-(-2))^2} \\

AB=\sqrt{16+144} \\

AB=\sqrt{160}\approx\boxed{12.65} \\

[/tex]

The answer is D.

Hope this helps.

r3t40

The correct answer is F. Quantitative data are numerical in​ nature, while qualitative data are categorical in nature.

Explanation:

In research and all the different fields that apply to it, the word "data" refers to information, values or knowledge that can be used to understand a specific situation or phenomenon. Additionally, data can be of two different types quantitative and qualitative, these differ in their nature, the phenomenons they described and the way they should be analyzed. Indeed quantitative data refers mainly to numerical data or information about quantities such as statistics that are especially useful in mathematics, science and similar that focus on numbers. On the other hand, qualitative data refers to data based on categories or qualities and because of this qualitative data is used in humanistic research, although both types of data can be combined to study a phenomenon. Considering this, the key difference between both types of data is "Quantitative data are numerical in​ nature, while qualitative data are categorical in nature".

Answer:

it is F

Step-by-step explanation:

F. Quantitative data are numerical in​ nature, while qualitative data are categorical in nature.

Answer:

A. f(x) = 6x + 9

Step-by-step explanation:

The given equation is:

y - 6x - 9 = 0

We have to write this equation in function notation with x as the independent variable. This means that y will be replaced by f(x) and all other terms will be carried to the other side of the equation to get the desired function notation.

y - 6x - 9 = 0

y = 6x + 9

f(x) = 6x + 9

Therefore, option A gives the correct answer.

Answer:

[tex]x^{2} \sqrt{x} \neq \sqrt[n]{x} \pi \alpha \frac{x}{y} x_{123}[/tex]

Step-by-step explanation:

Answer:

BD = 10

Step-by-step explanation:

Since AC is a tangent to the circle at B then ∠ABD = 90°

Using Pythagoras' identity in the right triangle ABD with hypotenuse AD

The square on the hypotenuse is equal to the sum of the squares on the other two sides, that is

BD² + AB² = AD²

BD² + 24² = 26²

BD² + 576 = 676 ( subtract 576 from both sides )

BD² = 100 ( take the square root of both sides )

BD = [tex]\sqrt{100}[/tex] = 10

Answer:

Approximately 5.19 hours.

Step-by-step explanation:

The question is asking that you solve for T (the amount of time spent with patients in a day). To do so, simply input the values which it has given you for your variables. We can substitute 16 for I as that is the doctor's preferred interval time and we can substitute 21 for N as that is the amount of appointments the doctors wishes to have per day.

[tex]16=1.08(\frac{T}{21} )[/tex]

To solve, start by multiplying both sides by 21.

[tex]336=1.08T[/tex]

Next, divide both sides by 1.08.

[tex]311.11=T[/tex]

Your answer comes out to 311.11 minutes. The question is asking for this to be translated into hours per day, which equates to approximately 5.19 hours.

The required hours per day is 5.19 hours a day needed by doctors to spend with patients.

Given that,

The interval​ time, I, in​ minutes, between appointments is related to the total number of minutes T that a doctor spends with patients in a​ day, and the number of appointments​ N, by the​ formula: I = 1.08 ​(T/N).
I = 16 minutes, N = 21.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,
I = 1.08 (T / N)
16 = 1.08 * T / 21
T = 16 * 21 / 1.08
T = 311.11 minutes
T = 311.11 / 60 hours
T = 5.19 hours

Thus, the required hours per day is 5.19 hours a day needed for doctors to spend with patients.

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Answer:

a=b

greater than

Step-by-step explanation:

Answer:

volumes of the cones are equal when (a=b)

If a > b, then the cross-sectional area of cone a is (GREATER THAN) is  the cross-sectional area of cone B at every level parallel to their respective bases.

Step-by-step explanation:

Answer:

In general you can choose the vertices at any arbitrary points but for easier computations and calculations we can choose 1 vertex at origin with co-ordinates [tex](0,0)[/tex] and it's adjacent vertex either on x-axis with co-ordinates [tex](x,0)[/tex] or on y-axis with ordinates [tex](0,y)[/tex]

Thus the coordinates of vertices become

Answer:

A.) −2y + 10

Step-by-step explanation:

−x − 2y = −10

Add 2y to both sides.

-x = 2y - 10

Multiply both sides by -1.

x = -2y + 10

Let's solve the system using the substitution method. We'll start by isolating \( x \) in the second equation.
The second equation is given by:
\[ -x - 2y = -10 \]
To isolate \( x \), we'll follow these steps:
1. Add \( 2y \) to both sides of the equation, which gives us:
\[ -x = 2y - 10 \]
2. Now, we multiply both sides by \( -1 \) to solve for \( x \), which gives us:
\[ x = -1(-2y + 10) \]
\[ x = 2y - 10 \]
The expression that we would substitute into the first equation for \( x \) is \( 2y - 10 \).
Therefore, the correct answer is:
C.) \( 2y - 10 \)

Answer:

750

Step-by-step explanation:

If we go up 1000 feet from sea level and then come down 250 from that, then we are being asked to compute the difference of 1000 and 250.

1000

-  250

---------

   750

We are 750 feet above sea level.

Answer:

1,250

Step-by-step explanation:

The answer would be 1,250 because you would add 1,000 and 250 to get the total elevation of the air craft.

Answer:

-4

Step-by-step explanation:

[√2(cos(3π/4) + i sin(3π/4))]⁴

(√2)⁴ (cos(3π/4) + i sin(3π/4))⁴

4 (cos(3π/4) + i sin(3π/4))⁴

Using De Moivre's Theorem:

4 (cos(4 × 3π/4) + i sin(4 × 3π/4))

4 (cos(3π) + i sin(3π))

3π on the unit circle is the same as π:

4 (cos(π) + i sin(π))

4 (-1 + i (0))

-4

Answer:

420 ways

Step-by-step explanation:

According to the given statement:

We want to divide the 10 dogs into three groups, one with 3 dogs, one with 5 dogs, and one with 2 dogs. How many ways can we form the groups such that fluffy is in the 3-dog group and nipper is in the 5-dog group.

In this way we have 8 dogs left.

2 spaces left in 3 dogs group

4 spaces left in 5 dogs group

and 2 spaces in 2 dogs group

Therefore:

= 8!/2!4!2!

= 8*7*6*5*4*3*2*1/2*4*3*2*2

= 8*7*6*5/2*2

= 1680/4

=420

It means there are 420 ways to from the groups....

Answer:

A statistics class with 36 students is arranged so that there are 6 rows with 6 students in each row, and the rows are numbered from 1 through 6. A die is rolled and a sample consists of all students in the row corresponding to the outcome of the die. This is not a simple random sample. It is a random sample only.

For the same class described in part (a), the 36 student names are written on 36 individual index cards. The cards are shuffled and six names are drawn from the top. This is a simple random sample. It is also a random sample.

For the same class described in part (a), the six youngest students are selected. This is not a simple random sample. It is also not a random sample.

Answer:

option 4 ⇒ 236 lb.

Step-by-step explanation:

Best explanation of the question is as shown in the attached figure.

we will use the parallelogram method to calculate resultant force.

to get the length of the resultant force ⇒ use the cosines law

The cosine law is a² = b² + c² - 2 * b * c * cos (∠A)

Applying at the question where b = F₁  , c = F₂  and  ∠A = ∠x

Given that F₁ = 100 pounds  , F₂ = 150 pounds  and  ∠x = 180° - 40° = 140°

∴ (Resultant force)² = 100² + 150² - 2 * 100 * 150 * cos (∠140) = 55481

∴ Resultant force = √55481 = 235.54 ≅ 236 pounds

The answer is option 4 ⇒ 236 lb.

Answer:

Step-by-step explanation:

The way you have written the first question may be what is confusing you. It should be written as

bn = 3*b_(n-1) + 2

So b2 =

b2 =3*b_(2 -1) + 2

b2 = 3*b1 + 2

b2 = 3*5 + 2

b2 = 15 + 2

b2 = 17

===========

b3 = 3b_(n _1) + 2

b_2 = 17 (from the step above)

b3 = 3*17 + 2

b3 = 51 + 2

b3 = 53

==========

b_4 = 3*b_3 + 2

b_4 = 3*53 + 2

b_4 = 159 + 2

b_4 = 161

Do you see how this works? You take the previous term, multiply by 3 and add 2 to get the current term. This one builds up rather quickly.

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Next Question

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tn = a + (n - 1)*d

t6 = a + (6 - 1)*d

t4 = a + 5d

4 = a + 5d    

t10 = a + 9d

Subtract t4 [4 = a + 3d ] from t10 written bellow

- 4 = a +  9d

4  = a + 5d

- 8 = 4d              Divide by 4

-8/4 = 4d/4

-2 = d

t6 = a + 5d

4 = a + 5*(-2)

4 = a - 10               Add 10 to both sides.

4 + 10 = a - 10 + 10

14 = a

tn = 14 + (n - 1)*d

Answer: d

Please don't use red. It is really hard to read.

Answer:

4, 10

Step-by-step explanation:

The value for the third side of the triangle is given by

b-a < n < b+a where a and b are the two other sides of the triangle and b>a

7-4 < n < 7+4

3 < n < 11

Since n is an integer

4 would be the smallest value and 10 would be the largest

Answer:

Smallest value of n = 4

Largest value of n = 10

Step-by-step explanation:

The sum of the shortest sides of a triangle must be greater than the longest side.

If 7 is the longest side, then:

n + 4 > 7

n > 3

n is an integer, so the smallest n can be is 4.

If n is the longest side, then:

4 + 7 > n

11 > n

n is an integer, so the largest n can be is 10.