There are 347 students at a college who have taken a course in calculus, 214 who have taken a course in discrete mathematics and 190 who have taken courses in both calculus and discrete mathematics.
A.How many students have taken a course in either calculus or discrete mathematics?
B.How many have taken calculus but not discrete mathematics?
C.How many have taken discrete mathematuics but not calculus?

Answer:

A factor

Step-by-step explanation:

Take the equation 2 x 4 = 8 as an example.

2 and 4 are multiplied together to get 8.

2 and 4 are factors, and 8 is the product.

Answer:

Step-by-step explanation:

The equation of a straight line can be represented in the slope-intercept form, y = mx + c

Where c = y intercept

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

If two lines are perpendicular, it means that the slope of one line is the negative reciprocal of the slope of the other line. The equation of the given line is

y=2x-4

Slope = 2

Therefore, the slope of the perpendicular line is -1/2

It passes through point (4,4)

We would determine the intercept, by substituting m = -1/2 , y = 4 and x = 4 into the slope intercept equation

y = mx + c

4 = -1/2 ×4 + c

4 = -2 + c

c = 4 + 2 = 6

The equation becomes

y = -x/2 + 6

Answer:

Step-by-step explanation:

The ratio of adult to children is determined by number of adult / number of children.

We want to determine the three ratios that are equivalent to 2 adults 5 children. So we will divide each of the given number of adults and children.

1) 8 adults 20 children = 8/20 = 2/5

2) 5 adults 8 children = 5/8

3) 20 adults 50 children = 20/50 = 2/5

4) 4 adults 10 children = 4/10 = 2/5

So the three ratios that are equivalent to 2 adults 5 children are

8 adults 20 children,

20 adults 50 children and

4 adults 10 children

Answer:

A rotation, then a dilation

Step-by-step explanation:

When two triangles are congruent, the three sides and angles will be the same.

A dilation is a type of transformation that works with scale factors and enlarges or reduces a figure, to create a new figure.

Now, the composition of transformations that will create a pair of similar but not congruent triangles are - a rotation, then a dilation.

A composition of a rotation followed by a dilation will create a pair of similar, but not congruent, triangles, option D.

The question asks which composition of transformations will create a pair of similar, but not congruent, triangles. In the realm of Euclidean geometry, certain transformations maintain the shape and size of geometric figures, while others maintain only the shape but not the size.

Among the choices given, a rotation followed by a reflection, a translation followed by a rotation, and a reflection followed by a translation will all produce congruent triangles, as they are types of isometries which preserve shape and size.

However, a rotation followed by a dilation is the correct composition that will result in triangles that are similar but not congruent. This is because rotation preserves the shape and size, but when followed by dilation, the size is changed while the shape remains the same, satisfying the condition of the question. Option D is correct.

Answer:

3

Step-by-step explanation:

To turn the word problem into an equation, when we read:

"I am thinking of a number" we write "x"

"when I double my number" we write "2x"

"and then subtract the result from 5" we write "5 - 2x"

"I get negative one" we write "-1 = 5 - 2x"

Now we solve for the number, which is x.

Equation: -1 = 5 - 2x

-1 = 5 - 2x

subtract 5 from both sides

-6 = -2x

divide both sides by -2

3 = x

The mathematical expression of the given phrase is 5 - 2x = -1 thus the number will be 3.

A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.

An expression is a mathematical proof of the equality of two mathematical expressions.

Let's say that number is x.

Double 2x

Subtract from 5

5 - 2x = -1

-2x = - 1 - 5

-2x = -6

x = 3

Hence "The mathematical expression of the given phrase is 5 - 2x = -1 thus the number will be 3".

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Answer:

40% or 0.4

Step-by-step explanation:

The optimal capital structure (OCS) of a firm is defined as "the proportion of debt and equity that results in the lowest weighted average cost of capital (WACC) for the firm"

The brief explanation of this is that OCS is the factor used by a company in maximising their stock price, and this generally calls for a Debt-to-capital or "Debit-to-equity" ratio.

From the table above, the company's stock ratio is highest or maximised at 37.75 (under Projected Stock Price Column)

This can be traced to 40% under Debt/Capital ratio column

Hence, the Debt/Capital Ratio of 40%,

Because it must equate to 100%, we say that the firm's optimal capital structure is 40% debt and 60% equity.

This is also the debt to capital ratio, where the firms WACC is minimized.

The optimal capital structure for Terrell Trucking Company is a 40% debt-to-capital ratio, indicating a mix of 40% debt and 60% equity. Assuming the WACC is minimized at the optimal capital structure, the company's WACC would also be minimized at a 40% debt-to-capital ratio.

In order to determine Terrell's optimal capital structure, we need to identify at what debt-to-capital ratio both the Earnings Per Share (EPS) and the stock price are highest. Based on the provided projections, the EPS and stock price are highest at a 40% debt-to-capital ratio. Therefore, the optimal debt-to-capital ratio for the company is 40%. This would indicate that Terrell's optimal capital structure is 40% debt and 60% equity.

Typically, the Weighted Average Cost of Capital (WACC) is minimized at the optimal capital structure. Assuming this holds true for Terrell Trucking Company, the company's WACC would also be minimized at a 40% debt-to-capital ratio.

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Answer:

The solution has been given in the attachment.

Step-by-step explanation:

Answer:The rate per week =

20.48/8 = 2.56 kilometers per week

Step-by-step explanation:

A construction crew has just built a new road. It took them 8 weeks to build 20.48 kilometers of road. To determine the rate at which the road was built, we would divide the total length of road that was built by the construction company by the number of weeks or days or even hours used in the construction.

The rate per week =

20.48/8 = 2.56 kilometers per week

If we want to find the rate per day,

1 week = 7 days

8 weeks will be 8×7 = 56 days

So the rate per day =

20.48/56 = 0.366 kilometers per day.

Answer:

B

Step-by-step explanation:

just multiply and add

Answer: c

Step-by-step explanation:

The minimum sample size does not depend on the size of the population

The size of the population, N, is NOT required to determine the minimum sample size for estimating a population mean, contrasting with the required elements like the desired confidence level, margin of error, and population standard deviation.

The question asks which factor is NOT required to determine the minimum sample size needed to estimate a population mean. The options are:

The correct answer is C. The size of the​ population, N. When estimating a population mean, the key factors required include the desired confidence level, the desired margin of error, and the value of the population standard deviation (sigma), but not necessarily the size of the population. This is especially true in cases where the population is very large or infinite, and the sample size needed for a specific confidence level and margin of error can be calculated without this information.

Answer:

Step-by-step explanation:

Pythagorean theorem is given as

a² +b² = c²

a² = c² - b²

a² = 252 – 202

a² = 625 – 400

a² = 225

a = √225

a = 15

Length of the missing side is 15

To find the value of the six trigonometric function

1) sin x = a/c

        = 15/25

     sin x   = 0.6,    x = sin⁻¹ 0.6 = 36.86

2) cos x = b/c

         = 20/25

       cos x  = 0.8,     x = cos⁻¹ 0.8 = 36.86

3) tan x = a/b

         = 15/20

     tan x   = 0.75,     x = tan⁻¹ 0.75 = 36.86

∴ Θ = 36.86°

4) csc x = c/a

         = 25/15

    csc x    = 1.67     x = csc⁻¹ 1.67

5) sec x = c/b

         = 25/20

      sec x   = 1.25     x = sec⁻¹ 1.25

6) cot x = b/a

        = 20/15

   cot x  = 1.33        x = cot⁻¹ 1.33

deltax = (56-0)/4 = 14

number of intervals 4

The intervals are:

(0,14),(14,28),(28,42),(42,56)

The Midpoint Rule =

f(7)+f(21)+f(35)+f(49)

[0.47577]+[-0.99159]+[-0.35892]+[0.65699]

deltax =14

sum = -0.21774

Multiplying by deltax = -3.0484

To approximate the integral of sin(x^2) dx from 0 to 5 using the Midpoint Rule with n=5, first calculate Δx = 1. Next, perform calculations with x values 0.5, 1.5, 2.5, 3.5, and 4.5. Finally, use the Midpoint Rule formula to calculate the approximated integral.

To solve this problem, you'll need to use the Midpoint Rule, which is a numerical method used to approximate definite integrals. In this case, we want to approximate ∫ from 0 to 5 of sin(x^2) dx with an n value of 5.

The Midpoint Rule can be represented as: Mn = Δx[f(x1) + f(x2) + ... + f(xn)], where Δx = (b-a)/n and each xi = a + (Δx/2) + (i-1)Δx.

Here, we'll first find our Δx = (5-0)/5 = 1, then calculate each xi and plug those into our function. Our xi values will be 0.5, 1.5, 2.5, 3.5, and 4.5. Finally, we plug into our formula and solve to find our approximated integral value.

A detailed and step-by-step solution would involve calculating each f(xi) with the xi values given above, and then adding these up

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Answer:

Capital expenditures

Step-by-step explanation:

The major difference between capital and revenue expenditures are usually seen by certain variables such as; the amount spent, frequency of the spend and whether the spend expands or improves the earning capacity, functionality  or operating efficiency of the asset under consideration.

For example, if the money spent on this building was just for painting and it is something that occurs every other year, then the amount spent would be referred to as operating expense.

In the question above, the money spent on the building does the following; materially prolong its life,increase its value. It is evident from these that such expense can be classified as capital expenditure.

Furthermore, this kind of expenditure cannot be carried out every year.

I hope this answer clears your doubt and improves your understanding of what is required.

Answer:

  False

Step-by-step explanation:

If we take this equation at face value, the expected utility bill is ...

  23.40 +0.4×2300

  = 23.40 +920

  = 943.40 ≠ 92.00

The equation does NOT predict a bill of $92.00.

The statement is false. Using the provided regression model (23.40 + 0.4x), the expected utility bill for a house of 2,300 square feet is $923.40, not $92.00.

The subject of this question lies within the field of Mathematics, specifically within statistics and regression analysis. In the given example, we have a study of 30 customers focusing on their utility bills. The regression model for this study is 23.40 + 0.4x, where 'x' denotes the number of square feet in a house. This model shows the relationship between the size of the house (in square feet) and the monthly utility bill.

To address the student's question, we use this model to calculate the expected utility bill for a customer who has a 2,300 square feet house by substituting 'x' with 2300. The calculation becomes: 23.40 + 0.4*2300 = 923.40, not $92.00. Therefore, the expected utility bill is approximately $923.40, not $92.00. So, the statement in the question is False.

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Answer: (39.424, 61.576)

Step-by-step explanation:

When population standard deviation([tex]\sigma[/tex]) unknown ,The confidence interval for population mean is given by :-

[tex]\overline{x}\pm t^*\dfrac{s}{\sqrt{n}}[/tex]

, where n= Sample size

[tex]\overline{x}[/tex] = sample mean.

s= sample standard deviation

[tex]t^*[/tex] = Critical t-value (two-tailed)

Given : n= 15

Degree of freedom= 14  [df=n-1]

[tex]\overline{x}=\ $50.50[/tex]

[tex]s^2=400\\\\\Rightarrow\ s=\sqrt{400}=20[/tex]

Significance level = [tex]\alpha=1-0.95=0.05[/tex]

For [tex]\alpha=0.05[/tex] and df = 14, the critical t-values : [tex]t^*=\pm2.1448[/tex]

Then the 95% confidence interval for population mean will be  :

[tex]50.50\pm (2.1448)\dfrac{20}{\sqrt{15}}\\\\=50.50\pm(2.1448)(5.1640)\\\\\approx50.50\pm11.076\\\\=(50.50-11.076,\ 50.50+11.076)\\\\=(39.424,\ 61.576)[/tex]

Hence, a 95% confidence interval for the average amount its credit card customers spent on their first visit to the chain's new store in the mall. : (39.424, 61.576)

The 95% confidence interval for the average amount its credit card customers spent on their first visit to the chain's new store in the mall is calculated using the sample mean ($50.50), sample size (15), sample standard deviation (20), and Z-value for a 95% confidence interval (1.96). The calculated interval is (-$1.11, $102.11).

To construct a 95% confidence interval for the average amount that the department store's credit card customers spent on their first visit to their new store, we would use the formula for a confidence interval:

CI = X-bar ± (Z-value * (s/√n)),

where X-bar is the sample mean = $50.50, n is the sample size = 15, s is the sample standard deviation = √400 = 20, and Z-value is the critical value from the Z-table which, for a 95% confidence interval, equals 1.96.

Plug these values into the formula,

CI = 50.5 ± (1.96 * (20/√15))

Using a calculator, the confidence interval comes out to (-$1.11, $102.11).

So, we are 95% confident that the average amount its credit card customers spent on their first visit to the chain's new store in the mall lies between $-1.11 and $102.11.

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Answer:

a) 100000

b) 90000

Step-by-step explanation:

We have the possibility of 10 digits

(0,1,2,3,4,5,6,7,8,9)

If there are no restrictions on the digit, there are 10 possibilities for each of the five digits

We then have;

10*10*10*10*10

= 10^5

= 100000

This means 100000 zip codes are possible if there are no restrictions.

b) If the first digit cannot be 3, there are 9 possibilities. This is because the possibility of the first digit being 3 is 1 out of 10. Therefore the possibility of not being 3 is 9 out of 10

The other four digits have 10 possibilities each.

So we have

9*10*10*10*10

= 90000

This means there are 90000 zip codes if the first digit does not start with 3

Answer:

15.87% of the invoices were paid within 15 days of receipt

Step-by-step explanation:

An invoice was paid an average of 20 days after it was received.

Mean = [tex]\mu = 20[/tex]

Standard deviation = [tex]\sigma = 5[/tex]

Now we are supposed to find what percent of the invoices were paid within 15 days of receipt i.e.P(x<15)

Formula : [tex]Z=\frac{x-\mu}{\sigma}[/tex]

At x = 15

Substitute the values

[tex]Z=\frac{15-20}{5}[/tex]

[tex]Z=-1[/tex]

Refer the z table for p value

So, p value = 0.1587

So, 15.87% of the invoices were paid within 15 days of receipt

Answer:

y = x + 1

Step-by-step explanation:

This line passes through (-1, 0) and (0, 1)  As we move from the first point to the second, x increases by 1 and y also increases by 1.  Therefore, the slope of this line is m = rise / run = 1 / 1, or m = 1.

Start with the general equation of a line y = mx + b.  Substitute 1 for m and 1 for b.  Then the equation of the line shown is:

y = x + 1

The equation of the graphed function is y = x + 1 .

The equation of the line can be written in the form ;

The slope of the line ; is the ratio of the rise to the run of the line ;

The intercept which is the value of y when x = 0 from.the graph is 1 .

Hence, the equation is :

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Answer:

Average rowing velocity of boat in still water is 4 miles per hour and average velocity of the current is 1 mile per hour.

Step-by-step explanation:

We are given the following in the question:

Let x be the average rowing velocity of boat in still water and y be the the average velocity of the current.

[tex]\text{Speed} = \displaystyle\frac{\text{Distance}}{\texr{Time}}[/tex]

The boat rowed 7.5 miles​ downstream, with the​ current, in 1.5 hours.

Velocity with the current =

[tex]=\text{average rowing velocity of boat in still water} + \text{ average velocity of the current} = x + y[/tex]

Thus, we can write the equation:

[tex]7.5 = (x+y)1.5\\x+y = 5[/tex]

The return trip​ upstream, against the​ current, covered the same​ distance, but took 2.5 hours.

Velocity against the current =

[tex]=\text{average rowing velocity of boat in still water} - \text{ average velocity of the current} = x - y[/tex]

Thus, we can write the equation:

[tex]7.5 = (x-y)2.5\\x-y = 3[/tex]

Solving, the two equations:

[tex]2x = 8\\x = 4, y = 1[/tex]

Thus, average rowing velocity of boat in still water is 4 miles per hour and average velocity of the current is 1 mile per hour.

Answer:

She should contribute $ 8369.38 ( approx )

Step-by-step explanation:

Let P be the amount invested by the other partner,

∵ The amount formula in compound interest,

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

Where,

r = annual rate,

n = number of compounding periods in a year,

t = number of years,

Here, r = 9% = 0.09, n = 4 ( quarters in a year ), t = 2 years,

Then the amount after 2 years,

[tex]A = P(1+\frac{0.09}{4})^{8}[/tex]

According to the question,

A = $ 10,000,

[tex]P(1+\frac{0.09}{4})^{8}= 10000[/tex]

[tex]P(1+0.0225)^8 = 10000[/tex]

[tex]\implies P = \frac{10000}{1.0225^8}\approx \$ 8369.38[/tex]

The statement is false. Multiple planes can be perpendicular to the same line through a given point.

The statement is False. If a line is perpendicular to a plane, it does not mean that it is the only plane perpendicular to the line.

There can be multiple planes perpendicular to the same line through a given point. For example, consider a line s passing through point Q and a plane M perpendicular to s at point Q. Now, we can also have another plane N perpendicular to line s at point Q, which is different from plane M. Therefore, the statement is false.

Answer: The speed of Bob is 56.8 km/hr.

Step-by-step explanation:

Let the speed of Bob be 'x'.

Let the speed of John be 'x-8'.

Distance covered = 230 miles

time = [tex]1\dfrac{1}{2}=\dfrac{3}{2}\ hr[/tex]

According to question, we get that

[tex]\dfrac{230}{x}-\dfrac{230}{x+8}=\dfrac{3}{2}\\\\230\dfrac{x+8-x}{x(x+8)}=\dfrac{3}{2}\\\\\dfrac{230\times 8}{x^2+8x}=\dfrac{3}{2}\\\\\dfrac{1840}{x^2+8x}=\dfrac{3}{2}\\\\1840\times 2=3x^2+24x\\\\3680=3x^2+24x\\\\3x^2+24x-3680=0\\\\x\approx 56.8\ km/hr[/tex]

Hence, the speed of Bob is 56.8 km/hr.

Answer:

  p(x) = x(x +5)(x -9)

Step-by-step explanation:

If r is a root, then (x -r) is a factor of the polynomial. For the given roots, the factorization is ...

  p(x) = (x -0)(x -(-5))(x -9)

  p(x) = x(x +5)(x -9)

Answer:

  A.  ZY=15

Step-by-step explanation:

Insufficient information is given about angles to make any statement about the value of p or the measures of any angles. (Eliminates B,C,D,E)

Side YZ corresponds to side FG. Since they are congruent, their measures are the same. This means ...

  2n -5 = n +5

  n = 10 . . . . . . . . add 5-n

YZ = ZY = 2·10 -5 = 15 . . . . . . matches choice A

Answer: B. 80

Step-by-step explanation:

We know that the formula to find the sample size is given by :-

[tex]n=(\dfrac{z^*\cdot\sigma}{E})^2[/tex]

, where [tex]\sigma[/tex] = population standard deviation.

E= margin of error

z*= Two -tailed critical z-value

Given : Confidence level = 98% =0.98

[tex]\alpha=1-0.98=0.02[/tex]

Population standard deviation : [tex]\sigma=300[/tex]

Also, from z-table for [tex]\alpha/2=0.01[/tex] (two tailed ), the critical will be = [tex]z^*=2.326[/tex]

Then, the required sample size must be :

[tex]n=(\dfrac{2.326\cdot300}{78})^2\\\\ n=(8.94615)^2\\\\ n=80.0336686391\approx80[/tex]  [To the nearest option]

Hence, the required sample size = 80

Hence, the correct option is option B. 80

Final answer:

To estimate the mean credit card balance owed by the bank's customers using a 98 percent confidence interval and a desired interval of $78, the sample size should be 725 customers.

Explanation:

To estimate the mean credit card balance owed by the bank's customers, we need to determine the sample size. We can use the formula for sample size calculation for a mean with a desired margin of error: n = (Z * σ / E)².

Here, Z is the Z-score for the desired confidence level, σ is the population standard deviation, and E is the desired margin of error. In this case, the Z-score for a 98 percent confidence level is approximately 2.33. Plugging in the values, we get: n = (2.33 * 300 / 78)² = 724.9.

Since we can't have a fractional sample size, we round up to the nearest whole number. Therefore, the bank should sample 725 customers.

Answer:

Yes. The outcomes can be classified into two categories, the trials are fixed, and the events are independent.

Step-by-step explanation:

Hope this helps!!

Answer:

Option c:

[tex]f(n)=4n+1[/tex]

Step-by-step explanation:

The functional relationship between two variables can be easily found if it's represented as a line.

Larry's online calculator collects these points

(1, 5), (2, 9), (3, 13), (4, 17)

We can see there is a linear relation because every time the first component increases by 1, the second increases by 4.

The equation of a line is given by

[tex]f(n)=m.n+b[/tex]

Where m is the slope of the line and can be computed as

[tex]\displaystyle m=\frac{d-b}{c-a}[/tex]

Where (a,b), (c,d) are two known points of the line. Let's use the first two points (1, 5), (2, 9)

[tex]\displaystyle m=\frac{9-5}{2-1}=4[/tex]

We now know that

[tex]f(n)=4n+b[/tex]

To compute the value of b, we use one of the points again, for example (1,5):

[tex]5=4(1)+b => b=1[/tex]

The relation is

[tex]f(n)=4n+1[/tex]

We can test our results by using other points like (3,13)

[tex]f(3)=4(3)+1=13[/tex]

And also

[tex]f(4)=4(4)+1=17[/tex]

All points belong to the same function or rule

[tex]f(n)=4n+1[/tex]

Answer:

  y = 2^(x–2) + 3

Step-by-step explanation:

The equation above is the one that is graphed. You can pick it from the offered choices by recognizing that the horizontal asymptote on the graph is y=3. That is 3 units above the horizontal asymptote of the parent exponential function. Hence, you must have ...

  y = (some exponential) +3

_____

Please note that the exponent indicator (^) and the grouping parentheses on the exponent are essential. Without those, the equation is that of the line y=2x+1, which is not what is graphed.

Answer: a. 120, b. 386, c. 176, d. 968.

Step-by-step explanation:

For a combination of any number, is given as

C n,r = n!/r!(n-r)!

Please note that "n,r" is a subscript, and the exclamation mark "!" is called factorial.

From the question, n = 10

EXACTLY 3 0s

10 combination 3

r is exactly 3, that is equal 3.

C 10,3= 10!/3!(10-3)! = 10!/3!7!= 120.

For clarification,

10!/3!7!=10×9×8/3×2×1 = 120.

You can also use a calculator to compute the factorials.

MORE 0s than 1s

There will be more 0s than 1s when < 5bits are 0s.

We have r<5

Therefore for r=4

C 10,4 = 10!/4!(10-4)!=10!/4!6!=210

r=3

C 10,3= 10!/3!(10-3)!=10!/3!7!=120

r=2

C 10,2=10!/2!(10-2)!=10!/2!8!=45

r=1

C 10,1=10!/1!(10-1)!=10!/1!9!=10

r=0

C 10,0=10!/0!(10-0)!=10!/0!10!=1

Summing the answers gives us our final answer

210+120+45+10+1= 386.

AT LEAST 7 1s

To get this combination, the value of r will be greater than or equal to 7

r>=7

We have,

r=7

C 10,7=10!/7!(10-7)!=10!/7!3!=120

r=8

C 10,8=10!/8!(10-8)!=10!/8!2!=45

r=9

C 10,9=10!/9!(10-9)!=10!/9!1!=10

r=10

C 10,10=10!/10(10-10)!=10!/10!0!=1

120+45+10+1= 176

AT LEAST 3 1s

the value for r will be greater than or equal to 3:

We can the values of r from 3 to 10.

r=3

C 10,3=10!/3!(10-3)!=120

r=4

C 10,4=10!/4!(10-4)!=10!/4!6!=210

r=5

C 10,5=10!/5!(10-5)!=10!/5!5!=252

r=6

C 10,6=10!/6!(10-6)!=10!/6!4!=210

r=7

C 10,7=10!/7!(10-7)!=10!/7!3!=120

r=8

C 10,8=10!/8!(10-8)!=10!/8!2!=45

r=9

C 10,9=10!/9!(10-9)!=10!/9!1!=10

r=10

C 10,10=10!/10!(10-10)!=10!/10!0!=1

Adding our answers gives 968.

The bits can be either 1 or 0. The total number of bit string for each specified case is:

Since the items are indistinguishable, their arrangements doesn't matter.

They can be chosen in [tex]^nC_r = \dfrac{n.(n-1).(n-2)...(n-(r+2)).(n-(r+1))}{r.(r-1).(r-2)...3.2.1} \: \rm (r \leq n)[/tex]

The bit string is of length 10.

Each bit can be in one of the two states, viz 0 or 1.

Evaluating the count of bit strings for given cases:

Think of it as if there are 10 seats and 3 people to sit on. They're going to be 0s. 3 seats can be chosen from 10 seats in [tex]^{10}C_3 = \dfrac{10\times 9\times 8}{3 \times 2\times 1} = 120[/tex] ways.

The three 0s are identical, so no intra-arrangement between them matters.

Thus, total 120 such strings exist.

It means, 0s can be 6,7,8,9, or 10 places.

Just similar to above case, 0s on x places out of 10 places can be in [tex]^{10}C_x[/tex] ways.

Thus, total such strings of 0s being more than 1s and being 10 bit strings are:

[tex]^{10}C_6 + ^{10}C_7 + ^{10}C_8 + ^{10}C_9 + ^{10}C_{10} =210+120+45+10+1=386[/tex]

At least seven 1s means either 7, 8, 9, or 10 ones.

Total count of such strings are:

[tex]^{10}C_7 + ^{10}C_8 + ^{10}C_9 + ^{10}C_{10} =120+45+10+1=176[/tex]

They are three or more ones. Total count of such strings is:

[tex]^{10}C_3 + ^{10}C_4 + ^{10}C_5+^{10}C_6 + ^{10}C_7 + ^{10}C_8 + ^{10}C_9 + ^{10}C_{10} =120 + 210 + 252 + 210+120+45+10+1=386+582=968[/tex]

Thus, the total number of bit string for each specified case is:

Learn more about combinations here:

https://brainly.com/question/11958814