The lateral area of a cone is 587 pi symbol cm^2. The radius is 32cm. Finf the slant height to the nearest tenth.

Step-by-step explanation:

To calculate the probability of getting at least four hearts when dealing five cards from a standard deck, we can use the concept of combinations and probability.

There are a total of 52 cards in a standard deck, and 13 of them are hearts (assuming no jokers). So the probability of drawing a heart on the first card is 13/52, or 1/4.

Now, there are two possible scenarios that would result in at least four hearts:

Four hearts and one non-heart: This can happen in C(13,4) * C(39,1) ways, where C(n, k) is the number of combinations of n items taken k at a time. The first part C(13,4) represents choosing 4 hearts out of 13, and the second part C(39,1) represents choosing 1 non-heart out of the remaining 39 cards. The total number of ways to choose 5 cards from 52 is C(52,5).

Five hearts: This can happen in C(13,5) ways, where C(13,5) represents choosing all 5 hearts out of 13.

So, the total number of favorable outcomes is C(13,4) * C(39,1) + C(13,5), and the total number of possible outcomes is C(52,5). Therefore, the probability of getting at least four hearts is:

P(at least 4 hearts) = (C(13,4) * C(39,1) + C(13,5)) / C(52,5)

Plugging in the values and simplifying, we get:

P(at least 4 hearts) = (C(13,4) * C(39,1) + C(13,5)) / C(52,5)

= (715 * 39 + 1287) / 2,598,960

= 27,885 / 2,598,960

≈ 0.0107566

So, the probability of getting at least four hearts when dealing five cards from a standard deck is approximately 0.0107566 or about 1.08%.

Answer:

101

Step-by-step explanation:

substitute 5 in the x:

=18(5)+11

=90+11

=101

Answer:

Step-by-step explanation:

C

The equation is expanding Pascal's triangle and the Binomial theorem

(x + 0.5)³ = x³/8 + 3x²/4 + 3x/2 + 1/8

(s + 4t)⁶ = s⁶ + 6s⁵(4t) + 15s⁴(4t)² + 20s³(4t)³ + 15s²(4t)⁴ + 6s(4t)⁵ + 4t⁶

(3a - 3b)⁴ = 81a⁴ - 324a³b + 486a²b² - 324ab³ + 81b⁴

(3m - 2n)⁵  = 243m⁵ - 810m⁴n + 1080m³n² - 720m²n³ + 240mn⁴ - 32n⁵

(a-4)⁵ = a⁵ - 20a⁴ + 160a³ - 640a² + 1280a - 1024

The binomial theorem formula for any positive integer n.

(x + y)n = nC0 xn + nC1 xn-1 by+ nC2 xn-2 y2 + … + nCn-1 x yn-1 + nCn x.

11) Using the Binomial Theorem, we have:

(x + 0.5)³ = C(3,0) x³(0.5)⁰ + C(3,1) x²(0.5)¹ + C(3,2) x¹(0.5)² + C(3,3) x⁰(0.5)³

= x³/2³ + 3x²/2² + 3x/2 + 1/2³

= x³/8 + 3x²/4 + 3x/2 + 1/8

12) Using Pascal's Triangle, we have:

(s + 4t)⁶ = C(6,0) s⁶(4t)⁰ + C(6,1) s⁵(4t)¹ + C(6,2) s⁴(4t)² + C(6,3) s³(4t)³ + C(6,4) s²(4t)⁴ + C(6,5) s(4t)⁵ + C(6,6) (4t)⁶

= s⁶ + 6s⁵(4t) + 15s⁴(4t)² + 20s³(4t)³ + 15s²(4t)⁴ + 6s(4t)⁵ + 4t⁶

13) Using Pascal's Triangle, we have:

(3a - 3b)⁴ = C(4,0) (3a)⁴(-3b)⁰ + C(4,1) (3a)³(-3b)¹ + C(4,2) (3a)²(-3b)² + C(4,3) (3a)(-3b)³ + C(4,4) (-3b)⁴

= 81a⁴ - 324a³b + 486a²b² - 324ab³ + 81b⁴

14)Using Pascal's Triangle, we have:

(3m - 2n)⁵ = C(5,0) (3m)⁵(-2n)⁰ + C(5,1) (3m)⁴(-2n)¹ + C(5,2) (3m)³(-2n)² + C(5,3) (3m)²(-2n)³ + C(5,4) (3m)(-2n)⁴ + C(5,5) (-2n)⁵

= 243m⁵ - 810m⁴n + 1080m³n² - 720m²n³ + 240mn⁴ - 32n⁵

15) Using Pascal's Triangle, we have:

(a-4)⁵ =  C(5,0) a⁵(-4)⁰ + C(5,1) a⁴(-4)¹ + C(5,2) a³(-4)² + C(5,3) a²(-4)³ + C(5,4) a(-4)⁴ + C(5,5) (-4)⁵

= a⁵ - 20a⁴ + 160a³ - 640a² + 1280a - 1024

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The equation is expanding Pascal's triangle and the Binomial theorem ,

[tex](x + 0.5)^3= x^3/8 + 3x^2/4 + 3x/2 + 1/8[/tex]

[tex](s + 4t)^6 = s^6+ 6s^5(4t) + 15s^4(4t)^2 + 20s^3(4t)^3 + 15s^2(4t)^4+ 6s(4t)^5 + 4t^6[/tex]

[tex](3a - 3b)^4 = 81a^4 - 324a^3b + 486a^2b^2- 324ab^3 + 81b^4[/tex]

[tex](3m - 2n)^5 = 243m^5 - 810m^4n + 1080m^3n^2- 720m^2n^3 + 240mn^4- 32n^5[/tex]

[tex](a-4)^5= a^5 - 20a^4 + 160a^3 - 640a^2+ 1280a - 1024[/tex]

What is the binomial theorem formula?

The binomial theorem formula for any positive integer n.

[tex](x + y)^n = nC_0 x^n + nC_1x^{n-1} y+ nC_2 x^{n-2} y_2 + … + nC_{n-1} x y^{n-1} + nC_n x.[/tex]

11) Using the Binomial Theorem, we have:

[tex](x + 0.5)^3 = C(3,0) x^3(0.5)^0 + C(3,1) x^2(0.5)^1 + C(3,2) x^1(0.5)^2 + C(3,3) x^0(0.5)^3[/tex]

=[tex]x^3/2^3 + 3x^2/2^2 + 3x/2 + 1/2^3[/tex]

= [tex]x^3/8 + 3x^2/4 + 3x/2 + 1/8[/tex]

12) Using Pascal's Triangle, we have:

[tex](s + 4t)^6 = C(6,0) s^6(4t)^0+ C(6,1) s^5(4t)^1+ C(6,2) s^4(4t)^2 + C(6,3) s^3(4t)^3 + C(6,4) s^2(4t)^4+ C(6,5) s(4t)^5 + C(6,6) (4t)^6[/tex]

= [tex]s^6 + 6s^5(4t) + 15s^4(4t)^2 + 20s^3(4t)^3 + 15s^2(4t)^4 + 6s(4t)^5 + 4t^6[/tex]

13) Using Pascal's Triangle, we have:

[tex](3a - 3b)^4 = C(4,0) (3a)^4(-3b)^0 + C(4,1) (3a)^3(-3b)^1 + C(4,2) (3a)^2(-3b)^2 + C(4,3) (3a)(-3b)^3 + C(4,4) (-3b)^4[/tex]

= [tex]81a^4 - 324a^3b + 486a^2b^2 - 324ab^3 + 81b^4[/tex]

14)Using Pascal's Triangle, we have:

[tex](3m - 2n)^5= C(5,0) (3m)^5(-2n)^0 + C(5,1) (3m)^4(-2n)^1 + C(5,2) (3m)^3(-2n)^2+ C(5,3) (3m)^2(-2n)^3 + C(5,4) (3m)(-2n)^4 + C(5,5) (-2n)^5[/tex]

= [tex]243m^5- 810m^4n + 1080m^3n^2 - 720m^2n^3 + 240mn^4 - 32n^5[/tex]

15) Using Pascal's Triangle, we have:

[tex](a-4)^5= C(5,0) a^5(-4)^0+ C(5,1) a^4(-4)^1 + C(5,2) a^3(-4)^2 + C(5,3) a^2(-4)^3 +C(5,4) a(-4)^4 + C(5,5) (-4)^5[/tex]

= [tex]a^5 - 20a^4 + 160a^3 - 640a^2 + 1280a - 1024[/tex]

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The value of x is given as follows:

x = 4.2 cm.

The value of x is obtained applying the proportions in the context of the problem.

The ratio between the volumes is given as follows:

3375/512 = 6.59

The side lengths are measured in units, while the volume is measured in cubic units, hence the proportion to obtain the value of x is given as follows:

8/x = cubic root of 6.59

8/x = 1.9

x = 8/1.9

x = 4.2 cm.

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The complete table is

Time (mins)              0     1      2     3     4      5     6     7     8     9     10  

Amount of air (ft³)   40   36   32   28   24    20   16   12    8      4     0

The rate of change refers to the speed at which a quantity is changing with respect to time or some other variable.

It is a measure of how quickly or slowly a quantity is increasing or decreasing, and it is often represented as the slope of a graph or function. To fill the table we need to know the rate of change per minute in the air. Using the rate of change we can fill the table as follows  

Here we have

A scuba tank started with 40 cubic feet of air and was empty after a 10-minute dive.

To complete the table, calculate the rate of change of the amount of air in the scuba tank.

We know that the scuba tank started with 40 cubic feet of air and was empty after a 10-minute dive, so we can use this information to find the rate of change:

Rate of change = (final amount - initial amount) / time

Rate of change = (0 - 40) / 10 = -4 ft³/min

The negative sign indicates that the amount of air in the scuba tank is decreasing over time, which makes sense since the diver is using up the air during the dive.

Using this rate of change, we can complete the table as follows:

For 1 min  = 40 ft³ - 4 ft³ = 36 ft³

For 2 min = 36 ft³ - 4 ft³ = 32 ft³

For 3 min = 32 ft³ - 4 ft³ = 28  ft³

Similarly, we can fill the table as given below

Therefore

The complete table is

Time (mins)              0     1      2     3     4      5     6     7     8     9     10  

Amount of air (ft³)   40   36   32   28   24    20   16   12    8      4     0

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This means that the median weight of a female child at 31.48 months is 28 pounds (approximately) base on logarithmic function.

Q1.1: The equation for the amount of money in the account after t years, compounded annually, can be given by:

A = P(1 + r/100)^t

where A is the amount of money in the account after t years, P is the principal amount invested, r is the annual interest rate, and t is the number of years.

Plugging in the values given in the problem, we get:

A = 1200(1 + 4.25/100)^t

Q1.2: We need to solve for t in the equation:

3000 = 1200(1 + 4.25/100)^t

Dividing both sides by 1200, we get:

2.5 = (1 + 4.25/100)^t

Taking the natural logarithm of both sides, we get:

ln 2.5 = t ln (1 + 4.25/100)

Solving for t, we get:

t = ln 2.5 / ln (1 + 4.25/100) ≈ 15.91 years

So, it will take approximately 15.91 years for the amount of money in the account to reach $3000.

Q2.1: To graph the function W = 7.5 + 5.9 ln(M + 1), we can use a graphing calculator or software. Here is a possible graph:

Graph of W = 7.5 + 5.9 ln(M + 1)

Q2.2: To find W ^−1(28), we need to solve the equation:

28 = 7.5 + 5.9 ln(M + 1)

Subtracting 7.5 from both sides, we get:

20.5 = 5.9 ln(M + 1)

Dividing both sides by 5.9, we get:

ln(M + 1) ≈ 3.474576

Taking the inverse logarithm of both sides, we get:

M + 1 ≈ e^3.474576

M ≈ e^3.474576 - 1 ≈ 31.48 months

So, W ^−1(28) ≈ 31.48 months. This means that the median weight of a female child at 31.48 months is 28 pounds (approximately).

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The solutions to the dividing fractions prompts are as follows:

6. 4/3

7. 2/13

8. 33/2

9. 24/35

10. 63/20

To solve the divisions, note that the second divisor is inversed and multiplied. For the following problems, the divisions can be gotten as follows:

6. 8/9 ÷ 2/3

= 8/9 × 3/2

=24/18

=4/3

7. 12/13 ÷ 6

= 12/13 × 1/6

= 12/78

=6/39

= 2/13

8.  11/5 ÷ 2/15

= 11/5 × 15/2

165/10

= 33/2

9. 6/7 ÷ 5/4

6/7 × 4/5

= 24/35

10. 7/2 ÷ 10/9

7/2 × 9/10

63/20

So, the above are ways to determine the step-by-step answers.

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a) The probability that an American chosen at random died as a passenger car occupant last year is 0.0042.

b) The probability that you died as a passenger car occupant last year is 0.0042

c) The probability that you will die as a passenger car occupant next year P(C) is 0.0042.

d) The probability that an American chosen at random will die as the result of a tornado next year is 0.0000018

e) The probability that you will die as the result of a tornado next year is 0.0000018

The given probabilities are determined as follows:

The probability that an American chosen at random died as a passenger car occupant last year is:

P(A) = 13,100 / 312,000,000

P(A) = 0.0042

b) The probability that you died as a passenger car occupant last year is:

P(B) = 13,100 / 312,000,000

P(B) = 0.0042

c) The probability that you will die as a passenger car occupant next year P(C) would be 0.0042 since the values do not change.

d) The probability that an American chosen at random will die as the result of a tornado next year is:

P(D) = 553  / 312,000,000

P(D) = 0.0000018

e) The probability that you will die as the result of a tornado next year, P(E) = 0.0000018

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Answer:

Yes, it is

Step-by-step explanation:

The probability that someone with a credit score of 650 or below defaulted on the loan is 0.14.

The probability that someone with a credit score of 650 or below defaulted on the loan is calculated below:

Probability = number of defaulters/ number of loan recipients

From graph:

The total number of defaulters = 30 + 30 + 30

The total number of defaulters = 90

The total number of loan recipients = 120 + 240 + 270

The total number of loan recipients = 630

Probability to default = 90/630

Probability to default = 0.14

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Answer:

52

Step-by-step explanation:

80% of 65 is 65 x 0.80

65 x 0.80 = 52

Therefore 52 seeds were planted.

the criteria is required to ensure communication competence is The message achieves the intended effect. Option A

Communicative competence is simply described as the ability to achieve communicative goals in an appropriate and socially way.

It is well organized and goal-oriented, this means that it involves the ability to evenly select and apply skills that are appropriate and are also effective in a given context.

The different components of communication competence are;

Hence, the message should  always be effective for the context.

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By sample distribution, (0.431,0.487) is Complete parts​ (a) through​ (d) below.

What does a statistical sample distribution mean?

An accurate probability distribution of a statistic is known as a sampling distribution, and it is created by repeatedly sampling a certain population. It depicts a spectrum of potential results for a statistic, such as the mean or mode of a variable, for a population.

Given

Favourable cases (X)=?

Sample size(n)=510

Sample proportion (p_hat)=X/n=0.459

X=np_hat=510*0.459=234.09=234

Confidence level(1-α)=99%=0.99

α=0.0

The critical value for  α=0.01 is Zc=2.576

The margin of error is E=Zc* √((p_hat(1-p_hat)/n))

E=2.576* √((0.459(1-0.459)/510))=0.0568

The 99% confidence interval for p

CI=(p_hat-E,p_hat+E)

CI=(0.459-0.0568,0.458+0.0568)

CI=(0.402,0.516)

Confidence level(1-α)=80%=0.80

α=0.20

The critical value for  α=0.2 is Zc=1.282

The margin of error is E=Zc* √((p_hat(1-p_hat)/n))

E=1.282* √((0.459(1-0.459)/510))=0.0283

The 80 % confidence interval for p

CI=(p_hat-E,p_hat+E)

CI=(0.459-0.0283,0.458+0.0283)

CI=(0.431,0.487)

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The number of cups of flour and sugar that Sam needs for the recipe will be 3.75 cups and 1.25 cups, respectively.

Given that:

A recipe for cookies makes 3 dozen cookies and uses 2 1/4 cups of flour and 3/4 cups of sugar.

The utilization of two or more additional numbers that compares is known as the ratio.

The expression that represents the 'n' dozen of cookies is given as,

⇒ n (2¹/₄) / 3 + n(3/4) / 3

⇒ n (2.25) / 3 + n(0.75) / 3

Put n = 5, then we have

⇒ 5 (2.25) / 3 + 5(0.75) / 3

⇒ 11.25/3 + 3.75/3

⇒ 3.75 + 1.25

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Answer:

12 = constant

5x = coefficient

Step-by-step explanation:

12 is a constant because it can not be changed.

5 is a coefficient because it can changed by the variable (x)

Answer:

64cm³

Step-by-step explanation:

( 4 x 4 x 4) cm x cm x cm

The figure given that has exactly two lines of symmetry is C. Rectangle.

A rectangle has two lines of symmetry.

A line of symmetry is a line that divides a shape into two equal parts that are mirror images of each other. In a rectangle, the two lines of symmetry run through the center of the rectangle, dividing it into two congruent halves. These lines of symmetry are perpendicular to each other and bisect both pairs of opposite sides of the rectangle.

Therefore, a rectangle has two lines of symmetry, one horizontal and one vertical, which make it a symmetrical shape.

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Answer:

Step-by-step explanation:

Answer:

7 + 2 = 149 here.

7 × 2 = 14, and 7 + 2 = 9.

Using the given zero . The three zeros of the polynomial function are 1 + i, 1 - i, 1/2, and 2.

If 1 + i is a zero of the polynomial function P(x), then its conjugate, 1 - i, must also be a zero of the polynomial, since complex zeros of polynomial functions with real coefficients always come in conjugate pairs.

To find the remaining zero, we can use polynomial division or synthetic division to divide P(x) by (x - 1 - i)(x - 1 + i), which is the quadratic factor corresponding to the two known zeros:

      2x^2 - 3x + 2

P(x) = --------------

       (x - 1 - i)(x - 1 + i)

Now we need to solve for the roots of the quadratic factor 2x^2 - 3x + 2. We can use the quadratic formula:

x = [3 ± sqrt(9 - 4*2*2)] / (2*2)

 = [3 ± sqrt(1)] / 4

 = 1/2 or 2

Therefore, the remaining zeros of P(x) are 1/2 and 2. The three zeros of the polynomial function are 1 + i, 1 - i, 1/2, and 2.

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The number of outcomes that contains blue shirts is 3

A tree diagram is a graphical representation of a hierarchy or branching structure, often used in fields such as mathematics, computer science, linguistics, and biology. It is called a tree diagram because it looks like a tree, with a single root node that branches out into multiple child nodes.

In mathematics, a tree diagram is used to represent the possible outcomes of a series of events or decisions, with each branch representing a different option or outcome.

The outcome for blue shirts is 3 because there is only small medium and large

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The areas of the region between the curves is -40/3square units.

We must first graph the curves in order to identify which one is on top in order to calculate the area of the region bounded by the curves for x in [0, 3]. y = x²− 4x + 1 and y = −x²+ 4x − 5

The vertex of the graph of y = x²− 4x + 1is at (2, -3), and it opens upward. The vertex of the graph of y =−x²+ 4x − 5 is at (2, -1), and it opens downward.

Thus, the curve y = x²− 4x + 1 is on top for x in [0, 1], and the curve y = −x²+ 4x − 5 is on top for x in [1, 3].

To determine which curve is on top, we can set them equal to each other and solve for x:

x²− 4x + 1 = −x²+ 4x − 5

2x² - 8x + 6 = 0

x² - 4x + 3 = 0

(x - 3)(x - 1) = 0

x = 1 or x = 3

Thus, the curves cross at x = 1 and x = 3. To find which curve is on top between these two points, we can test a point in between, such as x = 2:

y = x²− 4x + 1 = 1

y = −x²+ 4x − 5 = -1

Using integration, we can find the area of the region:

∫[0,1] (x²− 4x + 1) dx + ∫[1,3] (−x²+ 4x − 5) dx

= [(1/3)x³ - 2x² + x] from 0 to 1 + [(-1/3)x³ + 2x² - 5x] from 1 to 3

=[1/3-2+1]+[{-9+8-15}-{-1/3+2-5}]

=-2/3+-38/3

=-40/3 square units.

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the power tells you how many times the base is multiplied.

1) 3^4 = 3 x 3 x 3 x 3

= 81

Answer:

D) 50

Step-by-step explanation:

-100 <-45 < 20 < 50

Answer:

50

Step-by-step explanation:

any numbers approaching negative (before 0) in an increasing manner are the lowest, whereas numbers approaching positive in a increasing manner are the greatest.

Answer:

I think like 60∘, 60∘, 60 ∘ , 60 ∘ , and 120∘?

After making six monthly payments on her car loan, Ms. Hughes's savings account balance will decrease by $1,470.

To find the change in Ms. Hughes's savings account balance each month due to her car payment, we can divide the total change in balance for the year ($-2,940) by the number of months in a year (12):

Change in savings account balance each month = $2,940 / 12 = -$245

So, Ms. Hughes's savings account balance decreases by $245 each month due to her car payment.

To find the total change in Ms. Hughes's savings account balance after making six monthly payments on her car loan, we can multiply the change in savings account balance each month by the number of months (6):

Total change in savings account balance after six monthly payments = -$245 * 6 = -$1,470

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The summary of the 3 rules on segments are written below.

The three rules on segments in circles are:

1. When two chords intersect inside a circle, they create four line segments.

The product of the lengths of the two segments of one chord is equal to the product of the lengths of the two segments of the other chord.

2. When two secants intersect outside a circle, they create four line segments.

The product of the length of the secant segment and its external segment is equal to the product of the length of the other secant segment and its external segment.

3. When one secant and one tangent intersect outside a circle, they create three line segments.

The product of the length of the secant segment and its external segment is equal to the square of the length of the tangent segment.

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The ordered pair (1, 2) is a solution for the equation 4x + 2y = 8.

To find an ordered pair that is a solution for the equation 4x + 2y = 8, we need to find a pair of values for x and y that satisfies the equation when we substitute them into the equation.

One way to do this is to choose a value for x and then solve for y, or vice versa.

For example, we can choose x = 1 and then solve for y:

4x + 2y = 8

4(1) + 2y = 8

4 + 2y = 8

2y = 4

y = 2

So, when x = 1 and y = 2, the equation is satisfied:

4(1) + 2(2) = 8

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