Mathematics College

If you toss six fair coins, in how many ways can you obtain at least two heads?

Answers

Answer 1

1/3 that is the correct answer

Related Questions

32% of 300 is what number? A.96 B.64 C.32 D.90

Answers

32% = 0.32

300 * 0.32 =96

Answer is A

Bethany wants to estimate the value of (4.296 x 10^11) x (1.8614 x 10^-14). Which statement about the estimate is true?

A. The value will be greater than 1 because 4.296 x 10^11 is a very large number and multiplication always increases the size of a number.

B. The value will be greater than 1 because 4 x 2 = 8 and 8 is larger than 1.

C. The value will be less than 1 because (4.296 x 10^11) x (1.8614 x 10^-14) will be a negative number. All negative numbers are less than one.

D. The number will be less than 1 because when adding the exponents,
11 + (-14) = 3, and a number in scientific notation with a negative exponent is less than 1.

Answers

D. The number will be less than 1 because when adding the exponents,
11 + (-14) = 3, and a number in scientific notation with a negative exponent is less than 1.

[tex](4.296 * 10^{11}) * (1.8614 * 10^{-14})= \\ \\ 4.296*1.8614*10^{11+(-14)}=\\\\7.99657*10^{-3}= \\ \\ \cfrac{7.99657}{1000}=\\\\0.00799657 [/tex]

A health clinic has 3 1/2 quarts and 1 gallon of antiseptic wash in inventory.How many fluid ounces of antiseptic wash do they have on hand?

Answers

1 gallon is 128 fluid ounces;
4 quarts make 1 gallon.

Change the mixed unit volume of antiseptic to just one unit. Which you choose is your choice.

((3 1/2) -4)) quarts = ((7/2)+4)) quarts = (7+8/2) quarts = (15/2) quarts

15/2 quarts = 240 fluid ounces

Answer:

240 fluid ounces

Step-by-step explanation:

A health clinic has [tex]3\frac{1}{2}[/tex] quarts and 1 gallon of antiseptic wash in inventory.

We have to convert the unit of fluid in ounces.

1 quart = 32 ounces

1 gallon = 128 ounces

[tex]3\frac{1}{2}[/tex] quarts = [tex]3\frac{1}{2}[/tex] × 32 = 112 ounces

Total fluid of antiseptic wash = 112 + 128 = 240 fluid ounces

They have 240 fluid ounces of antiseptic wash in hand.

Mary is making Magic Marshmellow cake . The recipe calls for 3/4 cup of milk and 2 eggs per serving. The wants to make enough cake for 20 people . How much milk will Mary need?

Answers

[tex]\bf \begin{array}{ccllll} \textit{cups of milk}&serving\\ -----&-----\\ \frac{3}{4}&1\\ x&20 \end{array}\implies \cfrac{\frac{3}{4}}{x}=\cfrac{1}{20}\implies \cfrac{\frac{3}{4}}{\frac{x}{1}}=\cfrac{1}{20} \\\\\\ \cfrac{3}{4}\cdot \cfrac{1}{x}=\cfrac{1}{20}\implies \cfrac{3}{4x}=\cfrac{1}{20}\implies 3\cdot 20=1\cdot 4x\implies \cfrac{3\cdot 20}{4}=x[/tex]

and surely you know how much that is.

A pencil and a ruler cost 2.50 together. The ruler costs $1.00 more than the pencil. How much is the pencil

Answers

p + r = 2.50
r = p + 1

p + p + 1 = 2.50
2p + 1 = 2.50
2p = 2.50 - 1
2p = 1.50
p = 1.50/2
p = 0.75 <=== pencil cost 75 cents

r = p + 1
r = 0.75 + 1
r = 1.75 .....ruler cost 1.75

1.75 should be correct by basics of mathematics

500 is 10 times as much as

Answers

The answer is 50 because 50 times 10 is equal to 500.

50 is the answer!!!!!!!!!!

A list of elements from which the sample may be drawn is called a

Answers

A list of elements from which the sample may be drawn is called a "population"

How many lines of symmetry does the figure have?

0
1
2
3

Answers

only 1
so answer is

1
hope it helps

The figure shown is an arrow. The concept of symmetry is the means of being made up of corresponding parts facing each other or around an axis. To put it more simply, the arrow has to be divided into perfect halves, or pieces to have lines of symmetry. With this information at hand, you must come to the conclusion that the arrow has only 1 line of symmetry.

what is the greatest whole number that rounds to 54,300

Answers

Well it depends what you're rounding to.

If you're rounding to the nearest hundred, then it would be 54349, because once it becomes 54350, it'll round to 54400.

If you're rounding to the nearest ten, then it would be 54304, because once it becomes 54305, it'll round to 54310.

And then rounding to the nearest one, err, 54300.4.

Describe the two possible ways to use the angle of depression that is outside a right triangle to find the measure of an angle inside the triangle?

Answers

1) The angle of depression is complementary to up angle of the right triangle:

=> Angle of depression = 90° - up angle

=> up angle = 90° - angle of depression

2) The angle of depression is equal to the bottom angle of the right triangle.

=> bottom angle = angle of depression.

Bob's Skate Shop had a profit of $3,563 during the month of August. The company models its profit using P=x^2+10x-12
, where x is the number of skateboards the company sells. How many skateboards did the company sell during the month of August? A. 50 B. 55 C. 60 D. 75

Answers

[tex]x^2+10x-12 =3563 \\ x^2+10x-12 -3563=0 \\ x^2+10x-3575=0 \\ D=b^2-4ac=10^2-4*1*(-3575)=100+14300=14400 \\ x_{1,2}= \frac{-bб \sqrt{D} }{2a}= \frac{-10б \sqrt{14400} }{2}= \frac{-10б 120 }{2} \\ x_1= -65 \ \ \ \O \\ x_2=55[/tex]

The company sold 55 skateboards.

A student ID number is a letter of the alphabet followed by 2 digits. How many different IDs are possible if the digits can be repeated?

Answers

Final answer:

There are 2600 different possible student IDs when a student ID consists of one letter followed by two digits that can repeat, calculated as 26 possible letters multiplied by 10 possible digits for each of the two digit positions.

Explanation:

The question asks how many different student IDs are possible if an ID consists of a letter followed by two digits, with the digits being allowed to repeat. To calculate the possible combinations, we multiply the number of options for each component of the ID. There are 26 letters in the alphabet and 10 possible digits (0-9) for each of the two positions that follow the letter, allowing for repetition.

The calculation is therefore 26 letters × 10 digits × 10 digits = 2600 possible combinations. Each component is independent of the others, so this follows the fundamental principle of counting in combinatorics.

Pressure (in pounds per square foot) on a diver at a depth of "d" feet: "P" = 64d + 2112
Solve for "d"

Answers

p=64d+2112

Subtract 2112 on both sides
p-2112=64d

Divide all terms by 64
p/64-33=d

Rearrange
d=p/64-33

what is the distance between (-5,5) and (2,6) rounding to the nearest hundred

Answers

[tex]\bf \textit{distance between 2 points}\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ -5}}\quad ,&{{ 5}})\quad % (c,d) &({{ 2}}\quad ,&{{ 6}}) \end{array}\qquad % distance value d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2} \\\\\\ d=\sqrt{[2-(-5)]^2+[6-5]^2}\implies d=\sqrt{(2+5)^2+(6-5)^2} \\\\\\ d=\sqrt{7^2+1^2}\implies d=\sqrt{50}[/tex]

Math Mean Help Please!

Rounding to the nearest tenth, what is the mean of 100, 75, 40, 90, 80, 100, 92, 88, 80, 84, 100.

Answers

84.5 would be the answer if rounded to the nearest tenth

The correct answer is 84.5. I hope this helps and that i receive the brainliest answer. Have a great day:)

The equation of motion for a weight suspended from a particular spring is given by p(t)=2sint3+5cost3p(t)=2sin⁡t3+5cos⁡t3, where p(t)p(t) is the displacement from the equilibrium position in centimeters, and tt is the time elapsed in seconds. at what time does the weight first reach the equilibrium position?

Answers

Final answer:

To find the time at which the weight first reaches the equilibrium position, set the equation of motion equal to zero and solve for t.

Explanation:

The equation of motion for the weight suspended from the spring is given by p(t) = 2sin(t/3) + 5cos(t/3), where p(t) is the displacement from the equilibrium position in centimeters and t is the time elapsed in seconds. The weight first reaches the equilibrium position when the displacement p(t) equals zero. To find the time at which this occurs, we set the equation equal to zero and solve for t.

2sin(t/3) + 5cos(t/3) = 0

Using trigonometric identities, we can rewrite the equation as:

2sin(t/3) = -5cos(t/3)

Dividing both sides by cos(t/3), we get:

2tan(t/3) = -5

Therefore, to find the time at which the weight first reaches the equilibrium position, we need to solve the equation 2tan(t/3) = -5 for t.

The cost of a parking permit consists of a one-time administration fee plus a monthly fee. A permit purchased for 12 months costs $660. A permit purchased for 15 months costs $810. What is the administration fee?

Answers

Answer:

answer = 60

Step-by-step explanation:

It might be option A or D. Mine was D

at the beginning of the summer, Conan had $180 in the bank. Each week he deposits another $64 that he earns mowing lawns. Is his account balance proportional to the number of weeks since he started mowing lawns?

Answers

what's his account balance? give us a bit more information

Answer:

no, because the initial 180 gets in the way

Step-by-step explanation:

what is 37% of 600? what are the steps.

Answers

37% /100 = .37
.37 x 600 = 222
37% of 600 is 222

"of" means multiplication
It's asking you to multiply 37% to 600
First, you have to turn 37% into a decimal
To turn a percent into a decimal, you have to divide it by 100, or just simply move the decimal point two places to the left
You get 0.37
Now, multiply 0.37 and 600
0.37*600=222
hope this helps:)

What is the future value of a $1,500 investment, earning 10 percent interest
per period, after two periods? (Round your answer to the nearest cent.)

Answers

For 1 period
A=P(1+rt)
A=1500(1+(1*.1))
A=$1650
For 2 periods
A=$1800
The amount of interest earned each time is $150.

The formula of compound interest is
A=p (1+r)^t
A future value?
P present value 1500
R interest rate 0.1
T two periods 2
A=1,500×(1+0.1)^(2)=> A=1,815

How do you solve 18-n divded by 2 (which is underneath the 18-n) is less than or equal to 6?

Answers

[tex]\dfrac{18-n}{2}\leq6\\ 19-n\leq12\\ n\geq7[/tex]

If the following fraction is reduced, what will be the exponent on the p? -5p^5q^4/ 8p^2q^2

A. 5
B.4
C.3
D.2

Answers

[tex]\bf \left.\qquad \qquad \right.\textit{negative exponents}\\\\ a^{-{ n}} \implies \cfrac{1}{a^{ n}} \qquad \qquad \cfrac{1}{a^{ n}}\implies a^{-{ n}} \qquad \qquad a^{{{ n}}}\implies \cfrac{1}{a^{-{{ n}}}}\\\\ -------------------------------\\\\ \cfrac{-5p^5q^4}{8p^2q^2}\implies \cfrac{-5p^5q^4p^{-2}q^{-2}}{8}\implies \cfrac{-5p^5p^{-2}q^4q^{-2}}{8} \\\\\\ \cfrac{-5p^{5-2}q^{4-2}}{8}\implies \cfrac{-5\boxed{p^3} q^2}{8}[/tex]

Answer: D. 2

Step-by-step explanation:

need help with this inequality

Answers

answer is D
|x-4| </ 1

x-4 </ 1
and
x-4 >/ -1

+4 both sides

x </ 5
x >/ 3
this is shown in the graph

The hypergeometric distribution is used when samples are taken from an infinite population with replacement.

Answers

The hypergeometric distribution is used when samples are taken from an infinite population with replacement.
The statement is FALSE

The hypergeometric distribution describes the probability of a certain number of successes in samples taken without replacement from a finite population, not an infinite one as stated in the question.

The hypergeometric distribution is a statistical model used to calculate probabilities in experiments where samples are drawn without replacement from a finite population. Unlike the statement presented in the question, the hypergeometric distribution is not used for infinite populations nor for sampling with replacement; that would be the domain of the binomial distribution.

write in order from least to greatest

Answers

.021, 99/1000, .845 hope this helps

Quadrilateral ABCD is similar to quadrilateral EFGH the length of the three longest side in quadrilateral ABCD are 24 feet 16 feet and 12 feet long if the two shortest sides of quadrilateral EFGH feet long and 18 feet long how long is the fourth side on quadrilateral ABCD ?

Answers

check the picture below

solve for "x"

since we know the two smallest sides for EFGH are 9 and 18, 9 is the smallest of all, and 18 is the next small

thus, for the the quadrilateral ABCD, the smallest is "x" and the next small is given, is 12, since that's smaller than 16 or 24

When all sides of a quadrilateral are transformed, the resulting quadrilateral will be similar to the transformed quadrilateral. The fourth side of ABCD is 6 feet

We have the lengths of ABCD in descending order to be:

[tex]Side\ 1 = 24[/tex]

[tex]Side\ 2 = 16[/tex]

[tex]Side\ 3 = 12[/tex]

We have the lengths of EFGH in ascending order to be:

[tex]Side\ 4 = 9[/tex]

[tex]Side\ 3 = 18[/tex]

The missing side of ABCD is the fourth side, and it can be solved using the following equivalent ratios:

Side 4 : Side 3 of ABCD = Side 4: Side 3 of EFGH

Substitute the values of the known sides

[tex]Side\ 4 : 12 = 9 : 18[/tex]

Express as fraction

[tex]\frac{Side\ 4 }{ 12} = \frac{9}{ 18}[/tex]

Multiply both sides by 12

[tex]Side\ 4 = \frac{9}{ 18} \times 12[/tex]

[tex]Side\ 4 = \frac{1}{2} \times 12[/tex]

[tex]Side\ 4 = 6[/tex]

Hence, the fourth side of ABCD is 6 feet

Read more about similar quadrilaterals at:

https://brainly.com/question/85384

Find the general solution of the given system. dx dt = −6x + 4y dy dt = − 7 4 x + 2y

Answers

I assume the coefficient on [tex]x[/tex] in the second equation is [tex]-\dfrac74[/tex]. The coefficient matrix

[tex]\begin{bmatrix}-6&4\\\\-\frac74&2\end{bmatrix}[/tex]

has eigenvalues given by

[tex]\begin{vmatrix}-6-\lambda&4\\\\-\frac74&2-\lambda\end{vmatrix}=\lambda^2+4\lambda-5=(\lambda+5)(\lambda-1)=0[/tex]

The eigenvalues are thus [tex]\lambda_1=-5[/tex] and [tex]\lambda_2=1[/tex].

For the eigenvalue [tex]\lambda_1[/tex], the corresponding eigenvector [tex]\eta_1[/tex] satisfies

[tex]\begin{bmatrix}-1&4\\\\-\frac74&7\end{bmatrix}\begin{bmatrix}\eta_{1,1}\\\eta_{1,2}\end{bmatrix}=\begin{bmatrix}0\\0\end{bmatrix}[/tex]
[tex]\implies\eta_{1,1}=4\eta_{1,2}[/tex]

so that we can choose [tex]\eta_1=\begin{bmatrix}4\\1\end{bmatrix}[/tex].

For [tex]\lamda_2=1[/tex], we have

[tex]\begin{bmatrix}-7&4\\\\-\frac74&1\end{bmatrix}\begin{bmatrix}\eta_{2,1}\\\eta_{2,2}\end{bmatrix}=\begin{bmatrix}0\\0\end{bmatrix}[/tex]
[tex]\implies7\eta_{2,1}=4\eta_{2,2}[/tex]

and we can choose [tex]\eta_2=\begin{bmatrix}4\\7\end{bmatrix}[/tex] for the corresponding eigenvector.

Then the general solution to the ODE system is given by

[tex]\begin{bmatrix}x(t)\\y(t)\end{bmatrix}=C_1\begin{bmatrix}4\\1\end{bmatrix}e^{-5t}+\C_2\begin{bmatrix}4\\7\end{bmatrix}e^t[/tex]

) there are exactly 20 students currently enrolled in a class. how many different ways are there to pair up the 20 students, so that each student is paired with one other student

Answers

Assuming that "pair up students" means "divide up all 20 of the students into groups of two," and we regard two pairings as the same if and only if, in each pairing, each student has the same buddy, then I believe that your answer of 20! / [(2!)^10 * (10!)] is correct. (And I also believe that this is the best interpretation of the problem as you've stated it.)

There are at least two ways to see this (possibly more).

One way is to note that, first, we have to select 2 students for the first pair; that's C(20, 2) (where by C(20, 2) I mean "20 choose 2"; that is, 20! / (18! * 2!). )

Then, for each way of selecting 2 students for the first pair, I have to select 2 of the remaining 18 students for the second pair, so I multiply by C(18, 2).

Continuing in this manner, I get C(20, 2) * C(18, 2) * ... * C(2, 2).

But it doesn't matter in this situation the order in which I pick the pairs of students. Since there are 10! different orders in which I could pick the individual pairs, then I want to divide the above by 10!, giving me the answer

[C(20, 2) * C(18, 2) * ... * C(2, 2)] / 10!.

This is the same as your answer, because C(n , 2) = n(n - 1) / 2, so we can simplify the above as

[(20 * 19) / 2 * (18 * 17) / 2 * ... * (2 * 1) / 2] / 10!
= 20! / [2^10 * 10!]
= 20! / [(2!)^10 * (10!)].

Another way is to reason as follows:

1. First, arrange the 20 students in a line; there are 20! ways to do this
2. We can get a pairing by pairing the 1st and 2nd students in line together, the 3rd and 4th students together, etc.
3. But if I switch the order of the 1st and 2nd student, then this doesn't give a different pairing. I don't want to count both orderings separately, so I divide by 2!
4. The same argument from step 3 holds for the 3rd and 4th student, the 5th and 6th student, etc., so I need to divide by 2! nine more times
5. Finally, the particular order in which I selected the ten pairings are unimportant--for example, the following orderings don't produce different pairings:

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20
3, 4, 1, 2, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20

So I need to further divide by the number of ways I can arrange the ten pairs, which is 10!.

graph -3/4 passing through (1,4)

Answers

The equation is y=-3/4x+b
when x=1 then y=4
so -3/4+b=4
so b=19/4
hence y=-3/4x+19/4.

hello :
an equation is :
y - 4 = (-3/4)(x-1)

HELP PLZ? You want to help build an awards podium for a track meet. If the podium has the dimensions shown, what is its volume?

Answers

volume = l x w x h

area 1 = 3 x 1.5 x 2 = 9 cubic feet

area 2 = 2 x 1.5 x 2 = 6 cubic feet

area 3 = 1.5 x 1 x 2 = 3 cubic feet

9+6+3 = 18 cubic feet total

Answer:

The volume of Podium is: 18 cubic feet.

Step-by-step explanation:

The volume of Podium is equal to the volume of 3 cuboids of different heights.

We know that a volume of cuboid with length l, width b and height h is given by:

Volume= l×b×h

Hence,

Volume of cuboid numbered as 3 is:

Volume= 1×2×1.5= 3 cubic feet.

Volume of cuboid numbered as 2 is:

Volume=2×2×1.5=6 cubic feet.

Similarly volume of cuboid numbered as 1 is:

Volume= 3×1.5×2=9 cubic feet.

Hence, the Volume of Podium is:

3+6+9=18 cubic feet.

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