Math Sets. Answer 1-9 Below.

Answer:

120 is correct and the formula to be used is 10C₃ or 10C₇ both of which work out to 120

Step-by-step explanation:

That appears to be correct . Since only one of two possibilities exist for each toss, for 10 tosses we determine if 3 heads appear that would be the same as 7 tails appearing for the 10 tosses

Number of ways r heads can appear in n tosses is indeed nCr

For r= 3 heads and n = 10 tosses this would be

10C₃ = 120

This should be the same as 10C₇ which works out to 120 also

Answer:

D. 84 and 6 over 7 in2

Step-by-step explanation:

The surface area of the cylindrical mini muffin can be calculated as follows:

Surface area = 2πr^2 + 2πrh

where r is the radius of the circular base and h is the height of the cylinder.

Given that the diameter of the mini muffin is 2 inches, the radius can be calculated as 1 inch (since radius = diameter / 2).

So, r = 1 inch and h = 1 and 1/4 inches.

Substituting these values into the surface area formula, we get:

Surface area = 2 x (22/7) x 1^2 + 2 x (22/7) x 1 x (5/4)

= (44/7) + (55/7)

= 99/7

≈ 14.14 square inches

Therefore, the surface area of 1 mini muffin is approximately 14.14 square inches.

To wrap 6 mini muffins, we need to multiply the surface area of 1 mini muffin by 6:

Surface area of 6 mini muffins = 6 x 14.14

≈ 84.84 square inches

Rounding off to one decimal place, the minimum amount of paper needed to wrap 6 mini muffins is approximately 84.8 square inches, which is closest to option D, 84 and 6/7 in^2.

Answer: Draw 41 circles and then divide them among her five friends.

Step-by-step explanation:

(E) "Increase the sample size to 200 children"

To increase the statistical power in this context, where the program sponsors believe the program is effective, we need to consider methods that would increase the likelihood of detecting a statistically significant improvement in mathematics skills.

Statistical power is the probability of correctly rejecting the null hypothesis when it is false (i.e., detecting a true effect). In this case, the null hypothesis would be that there is no improvement in mathematics skills due to the program.

Among the options provided, the most appropriate method for increasing power would be to increase the sample size.

By increasing the sample size, we can reduce sampling variability and increase the precision of our estimates. This would lead to narrower confidence intervals and a higher likelihood of detecting a statistically significant improvement in mathematics skills if the program is indeed effective.

The other options, (A) "Use a two-sided test instead of a one-sided test," (B) "Use a one-sided test instead of a two-sided test," (C) "Use a = 0.01 instead of a = 0.05," and (D) "Decrease the sample size to 50 children," do not directly address the issue of increasing statistical power and may not necessarily improve the ability to detect a true effect.

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Answer:

Step-by-step explanation:

Assuming that the vectors are straight lines, NO.  If you're not convinced, try sketching this situation.

Answer:

-1875

Step-by-step explanation:

An arithmetic sequence has a common difference as a sequence. Here the common differnece is -11.

So our sequence so far looks like,

(57,46,35,24....). We know the last term of the sequence is -207 and we need to find the nth term of that series so we use arithmetic sequence

\(a _{1} + (n - 1)d \)

where a1 is the inital value,

d is the common differnece and n is the nth term.

We need to find the nth term so

\(57 + (n - 1)( - 11) = - 207\)

\((n - 1)( - 11) = - 264\)

\(n - 1 = 24\)

\(n = 25\)

So the 25th term of a arithmetic sequence is last term, now we can use the sum of arithmetic sequence

which is

\( \frac{a _{1} + a _{n} }{2} n\)

\( \frac{57 + ( - 207)}{2} (25) = \)

\( \frac{ - 150}{2} (25)\)

\( - 75(25) = - 1875\)

Answer:

-1875

Step-by-step explanation:

57 , 46 , ......... -207

\(First \ term = \ a_{1} = 57\\\)

common difference = d = second term - first term = 46 - 57 = -11

\(n^{th} \ term = -207\\\\a + (n-1)*d=t_{n}\)

57 + (n-1)* (-11) = -207

57 - 11n + 11 = -207

     -11n + 68  = -207

            -11n   = -207 - 68

             -11n  = -275

                 n = -275/-11

                n = 25

\(S_{n}=\dfrac{n}{2}(a_{1}+l)\\\\\\S_{25}=\dfrac{25}{2}*(57 + (-207) )\\\\\\ =\dfrac{25}{2}* (-150)\\\\\\= 25 *(-75)\\\\= -1875\)

Answer:

14, 18, 20

Step-by-step explanation:

You have to replace the number in the "s" column with the "s" in the problem. For example the first number in the table is 2 so you have to put 2 into the problem then add it with 12 and you get 14.

Answer:19, 81, 45

Step-by-step explanation:

The probability of having the first head at the k-th trial is 1/2.

The formula for the binomial distribution of probability is shown below. It can be used to determine the likelihood of getting K heads out of N coin tosses.

[nC k]* [pk]* [qn-k]

p= probability of receiving a head and

q= probability of having a tail.

Both p and q are 1/2.

As a result, the equation is [f12n! * f! r! * (n-r)!]

If you obtain exactly r successes, you also get (n - r) failures at the same time.

qn - rpr = P(getting r successes and n - r failures) (since the n trials are independent) Using the product theorem

There is no mention of the challenges from which the results were attained. There are nCr methods for selecting successful trials among r trials. The remaining (n - r) trials should be failures once the r trials that were picked for successes have been chosen. These nCr methods are incompatible. P(obtaining exactly r successes) in each of these nCr methods equals qn - rpr.

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The probability that an adult in the city is single is 14%.

In the given city, based on the survey results, the percentages of adults with different marital statuses are provided. To find the probability of an adult being single, we look at the percentage of single individuals, which is 14%. Therefore, the probability of an adult being single is 14%.

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Answer:

y = -2x - 8

Step-by-step explanation:

Find the slope using rise/run (y2 - y1) / (x2 - x1)

(-10 - 8) / (1 + 8)

-18/9

= -2

Next, plug in the slope and a point into the equation to find b:

y = mx + b

-10 = -2(1) + b

-10 = -2 + b

-8 = b

Now, plug this and the slope into the equation:

y = -2x - 8

Answer:

x = 5

Step-by-step explanation:

The diagram shows that the rhombus is split into two isosceles triangles, LKM and NMK.  

Thus, the three angles in triangle LKM are 110, (8x - 5), and (8x - 5).

Thus, we can solve for x by setting the sum of the measures of the three angles in triangle LKM equal to 180:

(8x - 5) + (8x - 5) + 110 = 180

(8x + 8x) + (-5 - 5 + 110) = 180

16x + 100 = 180

16x = 80

x = 5

Thus, x = 5

Optional step:

We can check that we've correctly solved for x by plugging in 5 for x in (8x - 5) twice for both angles, adding the result to 110, and seeing if we get 180 on both sides of the equation:

(8(5) - 5) + (8(5) - 5) + 110 = 180

(40 - 5) + (40 - 5) + 110 = 180

35 + 35 + 110 = 180

70 + 110 = 180

180 = 180

Thus, x = 5 is correct.

Step-by-step explanation:

first box on the left

r=4

d=8

circumference= 2π*4= 8π

area = π*4*4= 16π

Second box on the left

d=6

r= 3

circumference= 2π*3= 6π

area =π*3*3= 9π

third box on the left

A=36π

A=36πarea= π*r*r

A=36πarea= π*r*rr= 6

A=36πarea= π*r*rr= 6d=12

A=36πarea= π*r*rr= 6d=12circumference= 2π*6= 12 π

the last box

C=18π

C=18πC= 2π*r

C=18πC= 2π*rr= 9

C=18πC= 2π*rr= 9d=18

C=18πC= 2π*rr= 9d=18area= π*9*9= 81π

Answer:

Yes please upload the pic

Step-by-step explanation:

:)

Answer:

t = 4.5

Step-by-step explanation:

Distribute 3 to the parentheses:

3(t + 4) = 25.5

3t + 12 = 25.5

Subtract 12 from both sides:

3t = 13.5

t = 4.5

So, the answer is t = 4.5

Answer:

Expression 1: 16÷8 has the greatest value.

Step-by-step explanation:

16÷8 =2

whereas,

0.16÷8= 0.02

1.6÷8= 0.2

0.16÷0.8= 0.2

:)

Answer:

The lower first quartile is 7.25

Answer:

a, b, e,f

Step-by-step explanation:

i dont have one

Answer:

The equation is not true. It is actually c=30

Step-by-step explanation:

First you have to divide amount of money she's selling the candy bars for which is $2.50.

If her profit was $75, you want to know how much bars she sold, you will have to divide the amount of money she's selling the candy bars for and the amount she's earning which is $75 divided by $2.50 which is 30.

So c= 30

No, the point (1,4) is not a solution of the set of linear inequalities y > 5x + 1 and y ≥ (1/2)x - 1 since the point does not satisfy both inequalities.

To determine if a point is a solution, we can substitute the x and y values of the point into the inequalities and see if they are true.

For the first inequality, y > 5x + 1:
4 > 5(1) + 1
4 > 6
This is not true, since 4 is not greater than 6. So the point (1,4) is not a solution for the first inequality.

For the second inequality, y ≥ (1/2)x - 1:
4 ≥ (1/2)(1) - 1
4 ≥ 0.5 - 1

4 ≥ -0.5

This is true, since 4 is greater than -0.5.

But since the point does not satisfy both inequalities, it is not a solution for the set of linear inequalities.

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Using the Combination formula,

Total number of ways there to paint 10 hotel rooms in a hotel with five colours is 527 ways .

We have given that,

total number of rooms available for paint = 10

number of colour avaliabile for painting = 5

Atmost three rooms can be painted green i.e

the number of ways for atmost three rooms are painted green = ¹⁰C₃ + ¹⁰C₂ + ¹⁰C₁ = 120 + 45 + 10 = 175

similarly, the number of ways for atmost three rooms are painted red = 175

the number of ways for atmost three rooms are painted blue = 175

Now, one room is remained for painting and two colours are available for it

the number of painting the remained room with aany of two available colours i.e black and white

= 2 ways

thus , total ways to paint the 10 hotel rooms with five different paints are (175×3 +2) = 527

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SOLUTION:

Step 1:

In this question, we are given the following:

Consider this system of equations:

Step 2:

The details of the solution are as follows:

CONCLUSION:

The values of x that are the solutions to the system of equations are:

9514 1404 393

Answer:

  The central angle is about 8.7°.

Step-by-step explanation:

The relation between angle and arc length is ...

  s = rθ

where r is the radius, and θ is the central angle in radians.

  600 = 3950·θ

  θ = 600/3950 radians = (12/79)(180°/π)

  θ ≈ 8.7°

\(\textit{area of a rectangle}\\\\ A=Lw ~~ \begin{cases} L=length\\ w=width\\[-0.5em] \hrulefill\\ L=a+5\\ w=a-2\\ A=60 \end{cases}\implies 60=(a+5)(a-2) \\\\\\ 60=\stackrel{F~O~I~L}{a^2+3a-10}\implies 0=a^2+3a-70 \\\\\\ 0=(a+10)(a-7)\implies a= \begin{cases} -10\\\\ 7 ~~ \textit{\LARGE \checkmark} \end{cases}\)

notice, we didn't use the negative value, valid though as it is, because in this case "a" can't be negative.

Given:

The exponential function is:

\(R(x)=(5.3)^x\)

To find:

The domain of the given exponential function.

Solution:

We know that the general form of an exponential function is:

\(f(x)=ab^x\)

Where, a is the initial value and b is growth/decay factor.

This function is defined for all real values of x, so the domain of these type of functions is the set of all real number.

We have,

\(R(x)=(5.3)^x\)

Here, a is 1 and b is 5.3. This function is defined for all real values of x

Therefore, the domain of these type of functions is the set of all real number or it can be written as \((-\infty,\infty)\).

Answer:

64 feet squared

Step-by-step explanation:

Since it's a square, all sides have a length of 8 ft. Area is length x width, so simply multiply 8 by itself. 64 feet squared is therefore the answer.

Answer:  3 : 4

Step-by-step explanation:

I hope this helped if wrong I'm not sure what the answer is

Answer:what is the least common denominator of the fractions 2/3 and 3/5? HELP PLEASE

Step-by-step explanation:

Answer:

I think the LCM is 4/5

Step-by-step explanation: