use the binomial theorem to determine the number of ways 1, 2, 3, and 4 heads can occur when four fair coins are flipped

Answer:

Step-by-step explanation:

equation of The line L : y = -(1/2)x + 6

A(8 , b) ∈ L  then b = -(1/2)(8) +6 then b = -4 + 6 = 2

Therefore ,

A(8 , 2)

AB = 2

CD = 6

BC = 8

…………………………………………

Area of the trapezoid ABCD

= (CB÷2)×(AB + CD)

= (8÷2)×(6+2)

= 32

Answer:

Step-by-step explanation:

Triangle MNP is a right triangle with the following values:

Interior angles of a triangle sum to 180°. Therefore:

m∠M + m∠N + m∠P = 180°

m∠M + 58° + 90° = 180°

m∠M + 148° = 180°

m∠M = 32°

To find the measures of sides MN and NP, use the Law of Sines:

\(\boxed{\begin{minipage}{7.6 cm}\underline{Law of Sines} \\\\$\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}$\\\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are the angles. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides opposite the angles.\\\end{minipage}}\)

Substitute the values into the formula:

\(\dfrac{MN}{\sin P}=\dfrac{NP}{\sin M}=\dfrac{PM}{\sin N}\)

\(\dfrac{MN}{\sin 90^{\circ}}=\dfrac{NP}{\sin 32^{\circ}}=\dfrac{8}{\sin 58^{\circ}}\)

Therefore:

\(MN=\dfrac{8\sin 90^{\circ}}{\sin 58^{\circ}}=9.43342722...\)

\(NP=\dfrac{8\sin 32^{\circ}}{\sin 58^{\circ}}=4.99895481...\)

To find the perimeter of triangle MNP, sum the lengths of the sides.

\(\begin{aligned}\textsf{Perimeter}&=MN+NP+PM\\&=9.43342722...+4.99895481...+8\\&=22.4323820...\\&=22.43\; \sf units\; (2\;d.p.)\end{aligned}\)

Answer:

Step-by-step explanation:

soory

The area of a desk pad eight yards wide and 4/5 yards long is given as follows:

A = 0.3 yd².

Considering a rectangle of length l and width w, we have that:

The dimensions for this problem are given as follows:

Hence the area is given as follows:

A = 0.375 x 0.8

A = 0.3 yd².

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Answer:

15 + -12

Step-by-step explanation:

15 + -12 = -27 any positive plus a negative would be a negative while two positives equal a positive and two negatives equal a negative

The probability of landing on a 2 is 1/2, which is equivalent to 0.5 in decimal form. So, the correct answer is D. 0.5.

What is Probability ?

Probability can be defined as ratio of number of favourable outcomes and total number of outcomes.

The spinner has two equal sections labeled 2 and 3, so the probability of landing on a 2 is the ratio of the number of 2's to the total number of sections on the spinner.

Since there are two sections in total and one of them is labeled with a 2, the probability of landing on a 2 is:

Probability of landing on a 2 = Number of 2's / Total number of sections

Probability of landing on a 2 = 1 / 2

Therefore, the probability of landing on a 2 is 1/2, which is equivalent to 0.5 in decimal form. So, the correct answer is D. 0.5.

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Answer:

Option D

Step-by-step explanation:

In ΔHBC and ΔACB,

            Statements                      Reasons

1). CB ≅ CB (leg)                          1). Reflexive property

2). BA ≅ CH (Hypotenuse)         2). Additional information for the

                                                       congruence of two right triangles by HL

                                                       property.

3). ΔHBC ≅ ΔACB                       3). HL property of congruence

Option D will be the correct option.

Answer: x=-9

Step-by-step explanation: First, combine like terms. 3x+4-2x=-5

Then x+4 = -5

x=-9

The domain and the range of the function are (-∝, ∝) and (0, ∝), respectively

From the question, we have the following parameters that can be used in our computation:

The graph

The above graph is an exponential function

The rule of an function is that

The domain is the set of all real values

In this case, the domain is (-∝, ∝)

For the range, we have

Range = (0, ∝)

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The income elasticity of demand for tennis balls is -1.5. The negative sign indicates an inverse relationship between income and the quantity demanded of tennis balls, suggesting that tennis balls are an inferior good.

To calculate the income elasticity of demand, we need to use the formula:

Income Elasticity of Demand = Percentage change in quantity demanded / Percentage change in income

Given that incomes increase by 58% and the quantity demanded of tennis balls drops by 87%, we can plug these values into the formula:

Income Elasticity of Demand = (-87%)/58%

Simplifying the calculation:

Income Elasticity of Demand = -1.5

The income elasticity of demand for tennis balls is -1.5. The negative sign indicates an inverse relationship between income and the quantity demanded of tennis balls, suggesting that tennis balls are an inferior good.

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The missing points from the Column is:

Game Free-Throw Percentage:        60  20  60  80

Average Free-Throw Percentage:    70  60  55  56.67

Game       Game           Total              Game                              Average

               Result                               Free-Throw                       Free-Throw

                                                       Percentage                       Percentage

1                8/10              8/10                 80                                  80

2                 6/10            14/20               60                                  70          

3                1/5               15/25                20                                  60        

4                3/5              18/30                60                                  55        

5                8/10             26/40               80                                  56.67                                                          

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The question attached here seems to be incomplete, the complete question is

Fill in the columns with Dmitri's free-throw percentage for each game and his overall free-throw average after each game.

Game       Game Result         Total      Game Free-Throw Percentage    Average Free-Throw Percentage

1                        8/10                        8/10                   80                                                           80

2                        6/10                        14/20                    

3                        1/5                        15/25  

4                        3/5                        18/30  

5                        8/10                       26/40  

Answer:

d =  103

e =  22

f = 55

Step-by-step explanation:

ok so the angles on the other side 22 and 103 are equal to 2 of the angles on the other side

the whole line is equal to 180

103 + 22 = 125

180 - 125 = 55

d =  103

e =  22

f = 55

Answer:

d = 103

e= 22

f= 55

Step-by-step explanation:

the opposite side of d equals 103 and they are adjacent which means they have the same measure

same goes to e the opposite side of it equals 22

and then for f a full line measure equals 180

so 103+22= 125

180-125= 55

there you have it :)

Answer:

Mode: 60

Median: 30

Mean: 36.666

Step-by-step explanation:

Answer:

-72

Step-by-step explanation:

9*(-2)³ = 9*(-8) = -72

Answer:

(C) -72

Step-by-step explanation:

\(9^1*(-2)^3\)

Any number to the exponent of 1 is equal to themselves

\(= 9*(-2)^3\)

Solve the exponent and multiply

\(= 9*(-8)\\=-72\)

I hope this helps!

Answer:

Depends on how the X and Y values are oriented but if the X value is on the bottom and the Y is on the top, then the graph is decreasing

Step-by-step explanation:

Have a great day!

Answer:

decreasing

Step-by-step explanation:

Answer:

b is the answer of this puestion

1. The slope of the water table between the two wells can be calculated by determining the difference in water table levels and dividing it by the distance between the wells. 2. The slope of Deer Creek can be determined by calculating the difference in elevation between its source and the valley floor and dividing it by the length of the creek. 3. To determine the ground measurements corresponding to 3.5 inches on the map, we need to use the map's scale. The scale of 1:24000 means that 1 inch on the map represents 24000 inches on the ground.

1. To calculate the slope of the water table between the wells, we subtract the water table level at one well (100 feet) from the level at the other well (300 feet), resulting in a difference of 200 feet. Since the wells are half a mile apart (2640 feet), we divide the difference in water table levels by the distance between the wells, giving us a slope of approximately 0.076 ft/mi.

2. The slope of Deer Creek can be determined by subtracting the elevation of its source (2700 meters) from the elevation at the valley floor (1290 meters), resulting in a difference of 1410 meters. Since the creek flows for 8 kilometers, we divide the elevation difference by the length of the creek, giving us a slope of approximately 176.25 m/km or 0.176 m/m.

3. To determine the ground measurements corresponding to 3.5 inches on the map, we use the scale of 1:24000. Since 1 inch on the map represents 24000 inches on the ground, 3.5 inches on the map would represent 84000 inches on the ground, which is approximately 7000 feet or 1.32 miles.

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False. An n × n matrix that is orthogonally diagonalizable does not necessarily have to be symmetric. A matrix is said to be orthogonally diagonalizable if it can be expressed as PDP^T, where P is an orthogonal matrix and D is a diagonal matrix.

For a matrix to be symmetric, it must satisfy the condition A = A^T, where A^T denotes the transpose of A. While it is true that symmetric matrices are always orthogonally diagonalizable, the converse is not necessarily true. There exist non-symmetric matrices that can still be orthogonally diagonalized. An example of such a matrix is the following:

  [1  2]

A = [3 4]

This matrix is not symmetric, as A^T is:

  [1  3]

A^T = [2 4]

However, it is still orthogonally diagonalizable. The matrix A can be diagonalized as:

A = PDP^T, where P = [0.8507 -0.5257]

[0.5257 0.8507]

          and D = [-0.3723   0     ]

                    [ 0      5.3723]

Therefore, it is not necessary for an n × n matrix that is orthogonally diagonalizable to be symmetric.

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Answer: D. 50 students

pls give me brainliest.

Step-by-step explanation: First we find the area of the classroom which is worked out below and it is the shape of a rectangle;

Area of a rectangle = Length * Breadth

                               = 60 ft * 40 ft

                               = 2400 ft²

Now to find the number of students that she will allow in the classroom, we have to divide the area of the classroom which is 2400 ft²by the amount of space allocated to each student which will be;

=

= 50

This means she will  allow 50 students into her class.

With 82% confidence that the true average weight gain during the December holidays for the sampled adult population is between -1.25 pounds. and 1.47 pounds.

To find the 82% confidence interval for the mean weight gain over the holidays in December, you can use the following formula:

\(CI = xd ± t*(SDd/sqrt(n))\)

where:

xd = average weight change of sample (0.11 lb increase)

SDd = standard deviation of weight difference (5.25 lbs)

n = sample size (23)

t = the critical value of the t distribution with n-1 degrees of freedom and the desired confidence level (82% in this case)

You can use a t-table or a calculator to find the critical value of the t-distribution. With 22 degrees of freedom (n-1) and an 82% confidence level, the critical value is approximately 1.319.

Plugging in the given values ​​gives:

\(CI = 0.11 ± (1.319*(5.25/sqrt(23))) = (-1.25, 1.47)\)

Therefore, we can say with 82% confidence that the true average weight gain during the December holidays for the sampled adult population is between -1.25 pounds. and 1.47 pounds.

Note that the confidence intervals include zero. This means that we cannot reject the null hypothesis that there is no significant difference in weight between mid-November and he early-to-mid-January.

However, this does not necessarily mean no weight gain during his December vacation, as there is individual variation in weight change within the sample.  

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The population of bacteria 1 minute ago was 25 million.

If the population of bacteria is increasing at the rate of 100% every minute, this means that the population is doubling every minute. So, if the population is currently at 50 million, then 1 minute ago it was half that amount.

To find out the population of bacteria 1 minute ago, we can divide the current population by 2:

50 million / 2 = 25 million

This is because if the population is increasing at 100% every minute, this means that every minute the population is doubling. So, if the current population is 50 million, then it must have been half that amount 1 minute ago, since it would have only undergone one doubling period in that time.

It is important to note that this assumption of exponential growth may not hold true for all populations, and that there may be other factors that affect the growth rate of bacteria in real-world scenarios.

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Complete Question : in an experiment, the population of bacteria is increasing at the rate of 100 % every minute. the population is currently at 50 million. how much was the population of bacteria 1 minute ago?

The required expression represents the value in dollars of the coin n years after Hector found is \($c(n) = 190 \times (1.1)^n$\).

Let's call the percentage increase in value each year "r". We know that after one year, the coin was worth $209, which is 209/190 = 1.1 times what it was worth when Hector found it. So we can set up an equation:

\($190 \times (1 + r)^1 = 209$\)

Simplifying this equation,

\($1 + r = \sqrt[1]{\frac{209}{190}}$\)

1 + r = 1.1

r = 0.1

So the percentage increase in value each year is 10%. To find the value of the coin "n" years after Hector found it, we can use the formula:

\($c(n) = 190 \times (1 + r)^n$\)

Substituting the value we found for "r", we get:

\($c(n) = 190 \times (1.1)^n$\)

So the expression for the value of the coin "n" years after Hector found it is:

\($c(n) = 190 \times (1.1)^n$\)

Thus, required expression represents the value in dollars of the coin n years after Hector found is \($c(n) = 190 \times (1.1)^n$\).

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there are 54,633,624 different collections of 16 coins chosen at random that will contain at least 3 coins of each type.

We have three types of coins, and we need to choose at least 3 coins of each type from a collection of 16 coins.

Let's consider each type of coin separately.

For the first type of coin, we need to choose at least 3 coins from the available coins. There are 8 coins of this type, so the number of ways to choose at least 3 coins is the sum of the number of ways to choose 3, 4, 5, 6, 7, and 8 coins:

C(8,3) + C(8,4) + C(8,5) + C(8,6) + C(8,7) + C(8,8) = 969

Similarly, for the second type of coin, we also have 8 coins to choose from, and we need to choose at least 3 coins. So the number of ways to choose at least 3 coins is also 969.

For the third type of coin, we only have 6 coins to choose from, so the number of ways to choose at least 3 coins is:

C(6,3) + C(6,4) + C(6,5) + C(6,6) = 56

Now, we need to multiply the number of ways to choose coins of each type together, since these choices are independent.

969 x 969 x 56 = 54,633,624

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The time it took the penny to hit the ground is 9.56s.

The time it takes for a penny dropped from a height of 95 meters to hit the ground can be calculated using the equation for kinematic motion:

t =\(\sqrt {\frac {2h} {g}}\)

where:

t is the time it takes to fall

h is the height from which the penny is dropped (95 meters)

g is the acceleration due to gravity (9.8 m/s^2)

Plugging in the values, we get:

t = \(\sqrt {(2 \times \frac {95} { 9.8})}\)

t ≈ 9.56 seconds

So it would take approximately 9.56 seconds for a penny dropped from a height of 95 meters to hit the ground.

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Answer:

Yes, the lines on the graph at 3 and -3 a part  of the solution,

Step-by-step explanation:

The inequality \(|y| \leq 3\) contains all the values of \(y\) 3 units from the origin including the values 3 and -3.

Thus, the lines on the graph y =-3 and y = 3 are the part of the solution.

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Answer:

I do not understand this either lolll lolll

but I guess eq 1 = D

EQ 2 = B

EQ 3 = A

EQ 4= C

Answer:

I am solving it rn! one sec bro :)

Answer:

A

Step-by-step explanation:

Answer: nomial  data

Step-by-step explanation:

Answer:

3 7/10

Step-by-step explanation:

Answer:  \(0 \le p(a) \le 1\)

The smallest p(a) can get is 0. The largest is 1. Both endpoints are included.

Explanation:

I'm assuming p(a) refers to a probability. If so, then p(a) = 0 means there's a 0% chance of the event happening. On the opposite end of the spectrum, p(a) = 1 means there's a 100% chance of the event happening. Most probabilities will fall somewhere in between.

Examples: