24. You use math in day-to-day routines when grocery shopping, going to the bank or mall, and while cooking. How do you imagine you will use math in your healthcare career?

Answer:

[tex]48.5654 \textdegree[/tex]

Step-by-step explanation:

Let [tex]D[/tex] be the mid point of [tex]AB[/tex]

Now in [tex]\Delta ACD\ and\ \Delta BCD[/tex]

[tex]AC=CB \ (given)\\CD=CD \ (common\ side)\\AD=DB \ (D\ is\ mid\ point\ of\ AB)[/tex]

[tex]Hence\ \Delta ACD\cong\Delta BCD[/tex]

[tex]\angle A=\angle B\\\angle ACD=\angle BCD\\\angle ADB=\angle BDC[/tex]

[tex]\angle ADB+\angle BDC=180\\2\angle ADB=180\\\angle ADB=90[/tex]

[tex]in \Delta BCD\\\cos\angle B=\frac{BD}{BC}\\ =\frac{45}{2\times34}\\ =\frac{45}{68} \\\angle B=\cos^{-1}(\frac{45}{68} )\\\angleB=48.5654\textdegree[/tex]

Question:

At the city museum, child admission is $5.80 and adult admission is $9.30. On Monday, four times as many adult tickets as child tickets were sold, for a total sales of $1548.00. How many child tickets were sold that day?

Answer:

36 child tickets were sold

Solution:

Given that,

Cost of 1 child admission = $ 5.80

Cost of 1 adult admission = $ 9.30

Let "c" be the number of child tickets sold

Let "a" be the number of adult tickets sold

On Monday, four times as many adult tickets as child tickets were sold

Number of adult tickets sold = four times the number of child tickets

Number of adult tickets sold = 4(number of child tickets sold)

a = 4c ----- eq 1

They were sold for a total sales of $ 1548.00

number of child tickets sold x Cost of 1 child admission + number of adult tickets sold x Cost of 1 adult admission = 1548.00

[tex]c \times 5.80 + a \times 9.30 = 1548[/tex]

5.8c + 9.3a = 1548  ---- eqn 2

Let us solve eqn 1 and eqn 2 to find values of "c" and "a"

Substitute eqn 1 in eqn 2

5.8c + 9.3(4c) = 1548

5.8c + 37.2c = 1548

43c = 1548

c = 36

Thus 36 child tickets were sold that day

Answer:

-273

222

217

212

207

202

197

192

187

182

177

172

167

162

157

152

147

142

137

132

127

122

117

112

107

102

97

92

87

82

77

72

67

62

57

52

47

42

37

32

27

22

17

12

7

2

-3

-8

-13

-18

-23

-28

-33

-38

-43

-48

-53

-58

-63

-68

-73

-78

-83

-88

-93

-98

-103

-108

-113

-118

-123

-128

-133

-138

-143

-148

-153

-158

-163

-168

-173

-178

-183

-188

-193

-198

-203

-208

-213

-218

-223

-228

-233

-238

-243

-248

-253

-258

-263

-268

-273

Step-by-step explanation:

Answer:

[tex]u_{n} = a + (n - 1)d\\\\n = 100, a = 222, d = -5\\\\

Substitute the values in.\\\\

u_{100} = 222 + (100 - 1)(-5)\\\\

u_{100} = 222 + (99)(-5)\\\\

u_{100} = 222 + (99)(-5)\\\\

u_{100} = 222 +-495\\\\

u_{100} = -273[/tex]

Answer:

Area of rectangle = 128 square feet

Step-by-step explanation:

Given:- A rectangle with side(a)=16 feet, side (b) = [tex]\frac{1}{2}[/tex] that links to a square.

perimeter (p) = 48 feet.

To find:- area of the square of the rectangle=?

Now,

[tex]Perimeter\ of\ square\ (p) = (2\times a)+(2\times b)[/tex]

[tex]48=(2\times 16)+(2\times b)[/tex]

[tex]48=32+2b[/tex]

[tex]2b=48-32[/tex]

[tex]2b=16[/tex]

[tex]b=\frac{16}{2}[/tex]

[tex]b=8 feet[/tex] -------(equation 1)

(8 is half of square of 4=16, [tex]4^{2}=16,\ \frac{16}{2} = 8[/tex])

Now, to find the area of square:-

Area of square (A) = Length [tex]\times[/tex] breadth

Area of square (A)= side a [tex]\times[/tex] side b

A= 16 [tex]\times[/tex] 8

[tex]\therefore[/tex]A = 128 square feet

Therefore Area of rectangle = 128 square feet

Answer:

The correct option is D.

Step-by-step explanation:

It is given that a set of 15 different integers has median of 25 and a range of 25.

Median = 25

Median is the middle term of the data. Number of observations is 15, which is an odd number so median is

[tex](\frac{n+1}{2})th=(\frac{15+1}{2})th=8th[/tex]

8th term is 25. It means 7 terms are less than 25. Assume that those 7 numbers are 18, 19, 20, 21, 22, 23, 24. Largest possible minimum value of the data is 18.

Range = Maximum - Minimum

25 = Maximum - 18

Add 18 on both sides.

25+18 = Maximum

43 = Maximum

The greatest possible integer in this set 43.

Therefore, the correct option is D.

(a) 90% confidence interval for price: (6.35, 7.41), margin of error: $0.53.

(b) Sample size for desired error (E=$0.25): 131 farming regions.

(c) 90% confidence interval for cash value: ($190,500, $222,300), margin of error: $15,900.

Confidence Interval and Sample Size for Watermelon Price

(a) 90% Confidence Interval and Margin of Error:

Standard Error: σ / √n = 1.94 / √37 ≈ 0.32

Critical Value (90%): z(α/2) ≈ 1.645

Margin of Error: E = z(α/2) * σ / √n ≈ 0.32 * 1.645 ≈ 0.53

Lower Limit: x - E ≈ 6.88 - 0.53 ≈ 6.35

Upper Limit: x + E ≈ 6.88 + 0.53 ≈ 7.41

The 90% confidence interval is (6.35, 7.41)*, with a margin of error of $0.53.

(b) Sample Size for Desired Error:

Rearrange formula for sample size: n = (z(α/2) * σ / E)^2 ≈ (1.645 * 1.94 / 0.25)^2 ≈ 130.34

Round up to nearest whole number: n = 131 farming regions

(c) 90% Confidence Interval for Cash Value:

Convert tons to pounds: 15 tons * 2000 pounds/ton = 30,000 pounds

Apply confidence interval to total value: 30,000 * (6.35, 7.41) ≈ (190,500, 222,300)

Margin of error: 30,000 * 0.53 ≈ 15,900

The 90% confidence interval for the cash value is ($190,500, $222,300), with a margin of error of $15,900.

Therefore, (a) 90% confidence interval for price: (6.35, 7.41), margin of error: $0.53

(b) Sample size for desired error (E=$0.25): 131 farming regions

(c) 90% confidence interval for cash value: ($190,500, $222,300), margin of error: $15,900

Answer:it sent 6945 during the 30 day marketing campaign

Step-by-step explanation:

Their goal is to increase the number of emails sent per day by 15 each day. The rate at which they increased the number of mails sent is in arithmetic progression.

The formula for determining sum of n terms of an arithmetic sequence is expressed as

Sn = n/2[2a + (n - 1)d]

Where

a represents the first term of the sequence.

n represents the number of terms.

d = represents the common difference.

From the information given

a = 14

d = 15

n = 30

We want to find the sum of 30 terms, S30. It becomes

S30 = 30/2[2 × 14 + (30 - 1)15]

S30 = 15[28 + 435]

S30 = 6945

Answer:

$12

Step-by-step explanation:

The equation here is (18*2/3).

18 divided by 3 is 6.

6 multiplied by 2 is 12.

Hence, the answer is 12.

Answer:

K

Step-by-step explanation:

Values of x and y are either negative or positive, but not 0. Lets try to make each choice "negative", so we can eliminate it.

F. x - y

If y is greater than x in any positive number, the result is negative.

1 - 3 = -2

So, this can be negative.

G. |x| - |y|

Here, if y > x for some positive number, we can make it negative. Such as shown below:

|5| - |8|

= 5 - 8

= -3

So, this can be negative.

H.

|xy| - y

Here, if y is quite large, we can make this negative and let x be a fraction. So,

|(0.5)(10)| - 10

|5| - 10

5 - 10

-5

So, this can be negative.

J. |x| + y

This can negative as well if we have a negative value for y and some value for x, such as:

|7| + (-20)

7 - 20

-13

So, this can be negative.

K. |xy|

This cannot be negative because no matter what number you give for x and y and multiply, that result WILL ALWAYS be POSITIVE because of the absolute value around "xy".

So, this cannot be negative.

Final answer:

The expression that cannot be negative for all nonzero values of x and y is K. |xy|. This is because the absolute value of any number, including the product xy, is always nonnegative.

Explanation:

Among the given options, K. |xy| is the expression that cannot be negative for all nonzero values of x and y. The reason for this is that the absolute value of any real number, including the product xy, is always nonnegative. This is due to the definition of absolute value, which measures the magnitude or distance of a number from zero on the number line, disregarding the direction (positive or negative). Therefore, even if x or y or both are negative, resulting in a negative product, the absolute value symbol converts this to a positive value. This fundamental property of absolute values ensures that K. |xy| will always return a nonnegative result, making it impossible to be negative.

Answer:

neither

Step-by-step explanation:

(-3,1), (-7,-2)

Slope of the line containing point (-3,1), (-7,-2) is

[tex]slope = \frac{y_2-y_1}{x_2-x_1} =\frac{-2-1}{-7+3} =\frac{3}{4}[/tex]

Slope of the line containing point (2,-1), (8,4) is

[tex]slope = \frac{y_2-y_1}{x_2-x_1} =\frac{4+1}{8-2} =\frac{5}{6}[/tex]

Slope of both the lines are not same, so they are not parallel

the slope of both the lines are not negative reciprocal of one another

So they are not perpendicular

Hence they are neither parallel nor perpendicular.

Answer:

[tex]P_o = \frac{143000}{e^{-20*0.01303024661}}=110193.69[/tex]

And we can round this to the nearest up integer and we got 110194.  

Step-by-step explanation:

The natural growth and decay model is given by:

[tex]\frac{dP}{dt}=kP[/tex]   (1)

Where P represent the population and t the time in years since 1970.

If we integrate both sides from equation (1) we got:

[tex] \int \frac{dP}{P} =\int kdt [/tex]

[tex]ln|P| =kt +c[/tex]

And if we apply exponentials on both sides we got:

[tex]P= e^{kt} e^k [/tex]

And we can assume [tex]e^k = P_o[/tex]

And we have this model:

[tex]P(t) = P_o e^{kt}[/tex]

And for this case we want to find [tex]P_o[/tex]

By 1990 we have t=20 years since 1970 and we have this equation:

[tex]143000 = P_o e^{20k}[/tex]

And we can solve for [tex]P_o[/tex] like this:

[tex]P_o = \frac{143000}{e^{20k}}[/tex]   (1)

By 2019 we have 49 years since 1970 the equation is given by:

[tex]98000 = P_o e^{49k}[/tex]   (2)

And replacing [tex]P_o[/tex] from equation (1) we got:

[tex]98000=\frac{143000}{e^{20k}} e^{49k} =143000 e^{29k}[/tex]  

We can divide both sides by 143000 we got:

[tex]\frac{98000}{143000} =0.685 = e^{29k}[/tex]

And if we apply ln on both sides we got:

[tex]ln(0.685) = 29k[/tex]

And then k =-0.01303024661[/tex]

And replacing into equation (1) we got:

[tex]P_o = \frac{143000}{e^{-20*0.01303024661}}=110193.69[/tex]

And we can round this to the nearest up integer and we got 110194.  

Answer:

Slope intercept form -   y = −2x

Slope is m = −2  

Slope

Answer:

[tex]\displaystyle \frac{a^2 }{b^2}=\frac{4}{9}[/tex]

[tex]\displaystyle \frac{a}{b}=\frac{2}{3}[/tex]

[tex]\displaystyle \frac{a^3}{b^3}=\frac{8}{27}[/tex]

Step-by-step explanation:

Ratios and Proportions

The ratio between two numbers x and y is defined as x/y. It measures how many times y is contained in x. For example 12/8 = 1.5 means 12 is 1.5 times 8.

We have two key sets of data: the ratio between the surface areas of the cylinders and the fact that the radius and heights of the cylinders come in the same proportion.

First, we can easily compute the ratio of the surface areas

[tex]\displaystyle \frac{Area_1}{Area_2}=\frac{8\pi \ in^2 }{18\pi \ in^2}=\frac{4}{9}[/tex]

It gives us the relation  

[tex]\displaystyle \frac{a^2 }{b^2}=\frac{4}{9}[/tex]

Computing the square root

[tex]\displaystyle \frac{a}{b}=\frac{2}{3}[/tex]

Computing the cube

[tex]\displaystyle \frac{a^3}{b^3}=\frac{8}{27}[/tex]

Answer: Keyshia rode 16/21 miles

Step-by-step explanation:

The distance of Bay View Bike Path is 7/8 a mile.

Keyshia is riding her bike on Bay View Bike Path and Keyshia's bike got a flat tire 2/3 of the way down the path and she had to stop.

This means that the total distance that she rode before her bike got a flat tire would be

2/3 × 7/8 = 2/3 × 8/7 = 16/21 miles.

Converting 16/21 miles to decimal, it becomes 0.76 miles

Keyshia rode 7/12 of a mile before getting a flat tire.

To solve this question, we need to find the distance Keyshia rode before her bike got a flat tire.

From the information given, we know that the Bay View Bike Path is 7/8 of a mile long. Keyshia rode 2/3 of the way down the path before stopping.

To find how far Keyshia rode, we can multiply the length of the path by the fraction of the path she rode:

2/3 x 7/8 = (2 x 7)/(3 x 8) = 14/24 = 7/12

Therefore, Keyshia rode 7/12 of a mile before getting a flat tire.

Answer:

Part 1) [tex]\$106[/tex]

Part 2) [tex]\$53[/tex]

Part 3) [tex]\$212[/tex]

Part 4) [tex]\$132.50[/tex]

Part 5) [tex]\$1.06x[/tex]

Step-by-step explanation:

we have

Money in a particular savings account increases by about 6% after a year.

we know that

The simple interest formula is equal to

[tex]A=P(1+rt)[/tex]

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest  

t is Number of Time Periods

Part 1) How much money will be in the account after one year if the initial amount is $100

in this problem we have

[tex]t=1\ year\\ P=\$100\\ A=?\\r=6\%=6/100=0.06[/tex]

substitute in the formula above

[tex]A=100(1+0.06*1)[/tex]

[tex]A=100(1.06)[/tex]

[tex]A=\$106[/tex]

Part 2) How much money will be in the account after one year if the initial amount is $50

in this problem we have

[tex]t=1\ year\\ P=\$50\\ A=?\\r=6\%=6/100=0.06[/tex]

substitute in the formula above

[tex]A=50(1+0.06*1)[/tex]

[tex]A=50(1.06)[/tex]

[tex]A=\$53[/tex]

Part 3) How much money will be in the account after one year if the initial amount is $200

in this problem we have

[tex]t=1\ year\\ P=\$200\\ A=?\\r=6\%=6/100=0.06[/tex]

substitute in the formula above

[tex]A=200(1+0.06*1)[/tex]

[tex]A=200(1.06)[/tex]

[tex]A=\$212[/tex]

Part 4) How much money will be in the account after one year if the initial amount is $125

in this problem we have

[tex]t=1\ year\\ P=\$125\\ A=?\\r=6\%=6/100=0.06[/tex]

substitute in the formula above

[tex]A=125(1+0.06*1)[/tex]

[tex]A=125(1.06)[/tex]

[tex]A=\$132.50[/tex]

Part 5) How much money will be in the account after one year if the initial amount is $x

in this problem we have

[tex]t=1\ year\\ P=\$x\\ A=?\\r=6\%=6/100=0.06[/tex]

substitute in the formula above

[tex]A=x(1+0.06*1)[/tex]

[tex]A=x(1.06)[/tex]

[tex]A=\$1.06x[/tex]

This question is incomplete, here is the complete question;

Question:

A company's January 1, 2016 balance sheet reported total assets of $120,000 and total liabilities of $40,000. During January 2016, the following transactions occurred: (A) the company issued stock and collected cash totaling $30,000; (B) the company paid an account payable of $6,000; (C) the company purchased supplies for $1,000 with cash; (D) the company purchased land for $60,000 paying $10,000 with cash and signing a note payable for the balance. What is total stockholders' equity after the transactions above?

Answer: $110 000

Step-by-step explanation:

Company total assets = $120 000

Company liabilities = $40 000

Beginning equity = total assets - liabilities

Beginning equity = $120,000 − $40,000 = $80,000.

Only transaction (A) affects stockholders' equity.

Therefore, stockholders' equity = $80,000 + $30,000 = $110,000

Answer:

8:5

Step-by-step explanation:

Answer: 8 to 5

Step-by-step explanation:

5 females

13-5 males = 8 males

8 to 5

Answer:

The vertical component of velocity is 156 feet per second

The horizontal component of velocity 1491 feet per second .

Step-by-step explanation:

Given as :

The velocity of gun = v = 1500 feet per sec

The angle made by gun with horizontal = Ф = 6°

Let The vertical component of velocity = [tex]v__y[/tex]

Let The horizontal component of velocity = [tex]v__x[/tex]

Now, According to question

The vertical component of velocity = v sin Ф

i.e  [tex]v__y[/tex] = v sin Ф

Or , [tex]v__y[/tex] = 1500 ft/sec × sin 6°

Or , [tex]v__y[/tex] = 1500 ft/sec × 0.104

∴  [tex]v__y[/tex] = 156 feet per second

So, The vertical component of velocity = [tex]v__y[/tex] = 156 feet per second

Now, Again

The horizontal component of velocity = v cos Ф

i.e  [tex]v__x[/tex] = v cos Ф

Or , [tex]v__x[/tex] = 1500 ft/sec × cos 6°

Or , [tex]v__x[/tex] = 1500 ft/sec × 0.994

∴  [tex]v__x[/tex] = 1491 feet per second

So, The horizontal component of velocity = [tex]v__y[/tex] = 1491 feet per second

Hence,The vertical component of velocity is 156 feet per second

And The horizontal component of velocity 1491 feet per second . Answer

Final answer:

The horizontal component of the bullet's velocity is 1492 feet per second, and the vertical component is 157 feet per second, rounded to the nearest whole number, when fired from a gun at an angle of 6 degrees with a muzzle velocity of 1500 feet per second.

Explanation:

The student is asking to find the vertical and horizontal components of a bullet's velocity when fired from a gun at a specific angle. To solve this, we use trigonometric functions, specifically sine and cosine, since the bullet's velocity makes an angle with the horizontal axis. Given a muzzle velocity of 1500 feet per second and an angle of 6 degrees with the horizontal, the horizontal component (Vx) is V * cos(θ) and the vertical component (Vy) is V * sin(θ).

Calculating the horizontal component: Vx = 1500 * cos(6 degrees) = 1500 * 0.99452 ≈ 1492 feet per second.

Calculating the vertical component: Vy = 1500 * sin(6 degrees) = 1500 * 0.10453 ≈ 157 feet per second.

We round these to the nearest whole number as per the question's requirement, so the horizontal component is 1492 feet per second and the vertical component is 157 feet per second.

Answer:

it depends

Step-by-step explanation:

If you draw a green one then you would do better without it but if you draw a red you would do better putting it back

Answer

no

Step-by-step explanation:

just because

Answer:

I and II.

Step-by-step explanation:

Dot plots are charts that represent data points on a simple scale using filled circles. Stemplots allow plotting data by dividing it into stems (largest digit) and leaves (smallest digits). Both dot plots and stemplots are like histograms since they allow to compare data relating to only one variable, and are used for continuous, quantitive data, highlighting gaps, clusters, and outliers.    

Histograms use bars to represents amounts, with no space between the bars and the height of the bars is proportional to the frequency or relative frequency of the represented amount. We refer to the relative frequency of a case when this frequency is divided by the sum of all frequencies of the cases. The proportionality between the height of the bar and the frequency is right when the width (interval) of the bar is the same for everyone, on the contrary, the area of the bar would be proportional to the frequency of cases.      

Therefore, of all the above, the correct statements are I and II. Statement III is incorrect because relative heights are proportional to relative frequencies.        

I hope it helps you!                    

Both dotplots and stemplots can show features like symmetry, gaps, clusters, and outliers. The relative areas in a histogram correspond to relative frequencies. However, frequencies in a histogram cannot be determined from relative heights alone, but from the area of the bars.

The subject of this question pertains to the interpretation and understanding of various graphical representations in statistics. Let's examine each statement in turn:

https://brainly.com/question/33662804

#SPJ11

Answer:

100 kg

Step-by-step explanation:

Data provided in the question:

Initial total weight of the berries = 200 kg

Initial weight of water present = 99% of the weight

= 198 kg

therefore,

Initial weight of the solids in berries = 200 kg - 198 kg = 2 kg

After 2 days water was 98% of the total weight of the berries

Thus,

2% was solid which means 2 kg was 2% of the total weight of the berries

Thus,

2% of Total weight of berries after two days = 2 kg

or

0.02 × Total weight of berries after two days = 2 kg

or

Total weight of berries after two days = [ 2 ÷ 0.02 ] kg

or

Total weight of berries after two days = 100 kg

Answer:

100 kilograms!!!!

Step-by-step explanation:

First of all, let's find the variable and what it should represent.

Let's say m stands for the moisture in the berries.

Since the berries are 200 kg and the moisture in the berries is 99%, which is 198 kg. 2 kg remain, so we the left part of our equation will be :

m/(m+2).

The right part of our equation will be 0.98 because 0.98 is 98%, which is m.

m/(m+2)=0.98.

When we multiply m+2 on both sides, we get:

m=0.98m+1.96.

Subtracting 0.98m on both sides gives us 0.02m=1.96.

Dividing 0.02 on both sides gives us:

m=98.

The question is asking what is the total weight of the berries after two days, so we add 2 to 98, or 2+m, which is 100.

100 kilograms is the answer.

Hope this helped and thanks y'all!!!

- izellegz on instagram

Answer:

Water level after 24 hours will be [tex]\frac{3}{25}\ inches[/tex].

Step-by-step explanation:

Given:

Evaporate rate of water= 0.005 inches per hour.

We need to find the level of water after 24 hours.

now we know the in 1 hour the water evaporates from a pool at a rate of 0.005 inches.

So To find the water level after 24 hrs we will multiply the evaporation rate with total number of hours which is 24 and the divide by 1 hour we get.

Framing in equation form we get;

water level after 24 hrs = [tex]\frac{24 \times 0.005}1 = 0.12\ inches[/tex]

Now to convert the number in rational form we have to multiply and divide the number by 100 we get;

[tex]\frac{0.12\times 100}{100} = \frac{12}{100}=\frac{3}{25}\ inches[/tex]

Hence Water level after 24 hours will be [tex]\frac{3}{25}\ inches[/tex].

Answer:4th: 729 6th: 6561

Step-by-step explanation: Sorry, I’m not 100% sure but I will try to help out: :)

So 2nd term is 81 and you want the 4th and 6th term.

Common ratio is 3

I approached it like this:

81x3=243 (3rd Term)

243x3=729 (4th Term)

729x3=2187 (5th Term)

2187x3=6561 (6th Term)

So if this isn’t the correct way the only other way I can think to approach this is

81+3=84(3rd Term)

84+3=87(4th Term)

87+3=90(5th Term)

90+3=93(6th Term)

Hope this helps

Final answer:

The 4th term is 729 and the 6th term is 6561 in the given geometric sequence with a common ratio of 3, starting with the second term of 81.

Explanation:

To find the 4th and 6th terms in a geometric sequence, we use the formula for the nth term of a geometric sequence Tn = ar^(n-1), where a is the first term, r is the common ratio, and n is the term number.

Given that the second term is 81 and the common ratio (r) is 3, we can find the first term by using the second term's formula: T2 = ar^(2-1) = ar = 81, so a = 81/r = 81/3 = 27.

Now, to find the 4th term (T4), we substitute the values into the formula: T4 = ar^(4-1) = 27 * 3^(3) = 27 * 27 = 729.

Similarly, to find the 6th term (T6), we use the formula again: T6 = ar^(6-1) = 27 * 3^(5) = 27 * 243 = 6561.

In conclusion, the 4th term is 729 and the 6th term is 6561 in this geometric sequence.

Answer:

When you reflect a point across the line y = x, the x-coordinate and y-coordinate change places. If you reflect over the line y = -x, the x-coordinate and y-coordinate change places and are negated (the signs are changed). the line y = x is the point (y, x). the line y = -x is the point (-y, -x).

Answer:

(₁₀⁶¹)

Step-by-step explanation:

In order to select 'm' item from a given set of 'n' items, the binomial coefficient is commonly used. In this problem, there are card with numbers from 1 ... 52, if we have 'i' type of cards with the total number of [tex]x_{i}[/tex]. Then:

[tex]x_{i}[/tex] ∈ positive real numbers

0 ≤ [tex]x_{i}[/tex] ≤ 10

Therefore, if we use the Bose-Einstein theorem, the different methods of dealing with the cards are:

(₁₀⁵²⁺¹⁰⁻¹) = (₁₀⁶¹)

Final answer:

The number of different 10-card hands that can be dealt from a superdeck is calculated using the combination formula C(520, 10), which accounts for choosing 10 cards from 520 without considering the order.

Explanation:

To determine how many different 10-card hands can be dealt from a superdeck consisting of 10 standard decks of cards, we need to calculate the combination of 520 cards taken 10 at a time. Since the order of the cards does not matter, we use the combination formula:
C(n, k) = n! / (k! * (n - k)!)

where n is the total number of cards in the superdeck (520), and k is the number of cards in the hand (10). The factorial function, represented by an exclamation mark (!), means to multiply a series of descending natural numbers. Thereore:
C(520, 10) = 520! / (10! * (520 - 10)!)

This represents the number of ways to choose 10 cards from a superdeck of 520 cards without regard to the order.

Answer: here is the whole thing

1.  B

2. C

3. D

4. C

5. D

PLS MARK BRAINLIST

Answer:

[tex]6x^2-5x+5[/tex] should be subtracted.

Step-by-step explanation:

we find the polynomial that is subtracted from 7x^2-6x+5 to get the difference equal to x^2-x

7x^2-6x+5-polynomial=x^2-x

To get the polynomial subtract x^2-x from the given polynomial

[tex]7x^2-6x+5 - (x^2-x)=  7x^2-6x+5-x^2+x[/tex]

[tex]6x^2-5x+5[/tex]

So [tex]6x^2-5x+5[/tex] should be subtracted.

As your sample size grows larger, the n - 1 adjustment for the standard deviation has a smaller impact on the estimates of standard deviation.

Step-by-step explanation:

The average (mean) of sample's distribution seems to be the same as the distribution mean at which samples were taken. The means of mean distribution will not change. However, the standard deviations for the samples mean is the standard deviations of the primary distribution divided by square roots of the samples size.

The standard deviations of means decreases as the samples size increases. Likewise, when the samples size decreases, the standard deviations for the samples mean increases. So, there is a little impact on standard deviations estimation when sample size increases.

Answer:

[tex]a_n = 2^{\frac{n^2-1}{4} + 1} + \frac{2^{n^2} - \, 2^{\frac{n^2-1}{4} + 1}}{4}[/tex]

For n = 3, there are 134 possibilities

Step-by-step explanation:

First, lets calculate the generating function.

For each square we have 2 possibilities: red and blue. The Possibilities between n² squares multiply one with each other, giving you a total of 2^n² possibilities to fill the chessboard with the colors blue or red.

However, rotations are to be considered, then we should divide the result by 4, because there are 4 ways to flip the chessboard (including not moving it), that means that each configuration is equivalent to three other ones, so we are counting each configuration 4 times, with the exception of configurations that doesnt change with rotations.

A chessboard that doesnt change with rotations should have, in each position different from the center, the same colors than the other three positions it could be rotated into. As a result, we can define a symmetric by rotations chessboard with only (n²-1)/4 + 1 squares (the quarter part of the total of squares excluding the center plus the center).

We cocnlude that the total of configurations of symmetrical boards is [tex] 2^{\frac{n^2-1}{4} + 1} [/tex]

Since we have to divide by 4 the rest of configurations (because we are counted 4 times each one considering rotations), then the total number of configutations is

[tex]a_n = 2^{\frac{n^2-1}{4} + 1} + \frac{2^{n^2} - \, 2^{\frac{n^2-1}{4} + 1}}{4}[/tex]

If n = 3, then the total amount of possibilities are

[tex]a_3 = 2^{\frac{3^2-1}{4} + 1} + \frac{2^{3^2} - \, 2^{\frac{3^2-1}{4} + 1}}{4} =  134[/tex]